Trigonometrical Identities Concise Solutions Chapter-21 Class 10

Including Trigonometrical Ratio Complementary Angles and Use of Four figure Trigonometrical Tables

Trigonometrical Identities Concise Solutions Chapter-21 Class 10. Selina  Concise Solutions of Exercise – 21 (A), Exercise – 21 (B), Exercise –21 (C), Exercise – 21 (D), Exercise –21 (E) for Class 10th. Concise Maths Solutions Trigonometrical Identities Chapter-21 for ICSE Maths Class 10 is available here. All Solutions of Concise Selina Maths of Trigonometrical Identities Chapter-21 has been solved according instruction given by council. This Post is the  Concise Solutions of Trigonometrical Identities Chapter-21 for ICSE Maths Class 10th.

Trigonometrical Identities Concise Solutions Chapter-21 Class 10

The Solutions of Concise Mathematics Trigonometrical Identities  Chapter-21 for ICSE Class 10. Experience teachers Solved Chapter-21 Trigonometrical Identities  of  Concise Selina Maths  for class 10th ICSE board. Therefore the ICSE Class 10th Maths Solutions of Concise Selina Publishers is helpful on  various topics including Chapter-21 Trigonometrical Identities.

–:Select Topic :–

Exercise – 21 (A),

Exercise – 21 (B),

Exercise –21 (C)

Exercise – 21 (D),

Exercise – 21 (E),

Trigonometric Table

EXERCISE -21(A) Trigonometrical Identities Concise Selina Maths Solutions for ICSE Class 10

Prove the following Identities :

Question 1.

…………

Answer 1

Trigonometrical Identities EXE -21 A Ans 1

Question 2.

………..

Answer 2

Trigonometrical Identities EX-21 A Ans 2

Question 3.

……….

Answer 3

Trigonometrical Identities EX -21 A Ans 3

Question 4.

………..

Answer 4

Trigonometrical Identities EX -21 A Ans 4

Question 5.

sin4A – cos4 A = 2 sin2A-1 

Answer 5

L.H.S. = sin4 A – cos4A = (sin2A)2-(cos2A)2
= (sin2A + cos2A) (sin2A – cos2A)     [(a2 – b2 = (a + b) (a – b)]
and = 1 (sin2 A – cos2A) [∵ sin2A + cos2A = 1]
so = sin2 A – (1- sin2A) (∵ cos2A = 1 – sin2A)
therefore = sin2 A – 1 + sin2 A
hence = 2 sin2A-1 = R.H.S.

Question 6.

(1 – tan A)2 + (1 + tanA)2 = 2sec2A

Answer 6

LHS = (1 -tanA)2 + (1 +tanA)2
= 1 + tan2 A- 2 tan A + 1 + tan2 A + 2 tanA
and = 2 + 2 tan2 A = 2 (1+tan2A)
hence = 2 sec2A (∵ l+tan2A=sec2A)
= R.H.S.

Question 7.

Cosec4 A – cosec2 A = cot4 A + cot2 A

Answer 7

L.H.S. = cosec4 A -cosec2 A
= (cosec2A)2 – cosec2A
and = (1 + cot2A)2 – (1 + cot2A)
= 1 + cot4 A + 2 cot2A – 1- cot2A
hence = cot4 A + cot2 A = R.H.S.

Question 8.

sec A (1-sin A) (sec A + tan A) = 1

Answer 8

Trigonometrical Identities EX -21 A Ans 8

Question 9.

cosec A (1 + cos A) (cosec A – cot A) = 1

Answer 9

Trigonometrical Identities EX -21 A Ans 9

Question 10.

sec2 A + cosec2A = sec2 A cosec2 A

Answer 10

Trigonometrial Identities EX-21 A Ans 10

Question 11.

          …………

Answer 11

Trigonometal IdentitiesEX-21 A Ans 11

Question 12.

tan2A – sin2A = tan2 A. sin2 A

Answer 12

Trigonometrical Identities EX -21 A Ans 12

Question 13.

cot2 A – cos2 A = cos2 A. cot2 A

Answer 13

Trigonometrical Identities EX -21 A Ans 13

Question 14.

(cosecA + sinA) (cosec A – sinA) = cot2 A + cos2A

Answer 14

L.H.S. = (cosec A + sin A) (cosec A – sin A)
= (cosec2A – sin2 A) [∵ (a + b) (a – b) = a2– b2]
and = 1 + cot2 A – sin2 A = cot2 A + 1 – sin2A
= cot2 A + cos2 A (∵ 1-sin2A = cos2 A)
hence = R.H.S.

Question 15

(sec A – cosA) (sec A + cosA) = sin2 A + tan2A

Answer 15

L.H.S. = (sec A-cos A) (sec A + cos A)
= sec2 A – cos2 A
and = 1 + tan2A-cos2 A
= 1-cos2 A + tan2 A
so = sin2 A + tan2 A  (∵ 1- cos2A=sin2A)
hence = R.H.S.

Question 16.

(cos A + sin A)2 + (cos A – sin A)2 = 2

Answer 16

LHS = (cos A + sin A)2 + (cos A – sin A)2
= cos2 A + sin2 A + 2 cos A sin A + cos2 A + sin2 A – 2 cos A sin A
and = 2 sin2 A + 2 cos2 A
= 2 (sin2A+cos2A)
hence = 2 x 1=2 = R.H.S. (∵ sin2A + cos2 A = 1)

Question 17.

(cosec A – sinA) (sec A – cos A) (tan A + cot A) = 1

Answer 17

Trigonometrical Identities EX -21 A Ans 17 

Question 18.

……

Answer 18

Trigonometrical Identities EX -21 A Ans 18

Question 19.

……….

Answer 19

Trigonometrical Identities EX -21 A Ans 19

Question 20.

………..

Answer 20

Trigonometal IdentitiesEX-21 A Ans 20

Question 21.

…………..
(sin A + cosec A)2 + (cos A + sec A)= 7 + tan2 A + cot2 A

Answer 21

L.H.S. = (sin A + cosecA)2 + (cosA+ secA)2
= sin2 A + cosec2 A + 2 sin A cosec A + cos2 A + sec2 A + 2 cos A sec A
and = sin2 A+cosec2 A+2 sin A x \frac { 1 }{ sinA } + cos2 A+sec2A + 2cosA x \frac { 1 }{ cosA }
= sin2A + cos2 A + cosec2 A + sec2A+ 2 + 2   (∵ sin2 A + cos2A= 1)
so = 1 +cosec2A + sec2A + 4
= (1 + cot2 A) + (1 + tan2 A) + 5 [∵ cosec2A = 1 + cot2 A and sec2 A = 1 + tan2A]
hence = 1 + cot2 A + 1 + tan2 A + 5
= 7 + tan2A + cot2A = R.H.S.

Question 22.

sec2A. cosec2A = tan2A + cot2A + 2

Answer 22

Trigonometal IdentitiesEX-21 A Ans 20

Question 23.

……..

Answer 23

Trigonometrial Identities EX-21 A Ans 23

Question 24.

………..

Answer 24

Trigonometrial Identities EX-21 A Ans 24

Question 25.

…………

Answer 25

Trigonometrical Identities EX -21 A Ans 25

Question 26.

………….

Answer 26

Trigonometrial Identities EX-21 A Ans 26

Question 27.

………….

Answer 27

Trigonometal IdentitiesEX-21 A Ans 27

Question 28.

…………

Answer 28

Trigonometrial Identities EX-21 A Ans 28

Question 29.

…………..

Answer 29

Trigonometrical Identities EX -21 A Ans 29

Question 30.

…………..

Answer 30

Trigonometrical IdentitiesEXE -21 A Ans 30

Question 31.

……………

Answer 31

Trigonometrical Identities EX -21 A Ans 31

Question 32.

………….

Answer 32

Trigonometrical Identities EX -21 A Ans 32

Question 33.

……………

Answer 33

Trigonometrical Identities EX -21 A Ans 33

Question 34.

……………

Answer 34

Trigonometrical Identities EX -21 A Ans 34

Question 35.

………………

Answer 35

Trigonometrical Identities EX -21 A Ans 35

Question 36.

…………..

Answer 36

Trigonometal IdentitiesEX-21 A Ans 36

Question 37.

………….

Answer 37

Trigonometrical Identities EX -21 A Ans 37

Question 38.

(1 +cot A-cosec A) (1 + tan A + sec A) = 2

Answer 38

Trigonometrical Identities EX -21 A Ans 38

Question 39.

………..

Answer 39

Trigonometrical Identities EX -21 A Ans 39

Question 40.

……………

Answer 40

Trigonometal IdentitiesEX-21 A Ans 40

Question 41.

…………..

Answer 41

Trigonometrical IdentitiesEXE -21 A Ans 41

Question 42.

………….

Answer 42

Trigonometrical IdentitiesEX-21 A Ans 42

Question 43.

………….

Answer 43

Trigonometrical IdentitiesEX-21 A Ans 43

Question 44.

…………

Answer 44

Trigonometrical Identities EX -21 A Ans 44

Question 45.

…………

Answer 45

Trigonometrical IdentitiesEX-21 A Ans 45

Question 46.

…………..

Answer 46

Trigonometrical Identities EX -21 A Ans 46

Question 47.

……………

Answer 47

Trigonometrical IdentitiesEX-21 A Ans 47

Question 48.

…………..

Answer 48

Trigonometal IdentitiesEX-21 A Ans 48

 EXERCISE – 21 (B) Solutions of Selina Concise Mathematics Chapter-20 Trigonometrical Identities 

Question 1.

Prove that: 

(i)…

(ii)…….

(iii)………

(iv)………

(v)………

(vi)……..

(vii)…….

(viii)…….

(ix)……….

Answer 1

(i)

Trigonometrical Identities EX -21 B Ans 1

(ii)

Trigonometrical Identities EX -21 B Ans 1 ii

(iii)

Trigonometrical Identities EX -21 B Ans 1 iii

(iv)

Trigonometrical Identities EX -21 B Ans 1 iii

(v)

Trigonometrical Identities EX -21 B Ans 1 v

(vi)

Trigonometrical Identities EX -21 B Ans 1 vi

(vii)

Trigonometrical Identities EX -21 B Ans 1 vii

(viii)

Trigonometrical-Identities-EX-21-B-Ans-1-viii

(ix)

Trigonometrical-Identities-EX-21-B-Ans-1-ix

Question 2.

If xcosA + ysinA = m and xsinA-ycosA = n, then prove that: x2+y2 = m2 + n2

Answer 2

x cos A + y sin A = m    …(i)
x sin A – y cos A = n     ….(ii)
squaring (i) and (ii)
x2 cos2 A + y2 sin2 A + 2 xy cosA sinA = m2
x2 sin2 A + y2 cos2 A – 2 xy cos A sin A = n2
Adding we get,
x2 (sin2 A + cos2 A) + y2 (sin2 A + cos2 A) = m2+n2
∴ x2+y2 = m2 + n2(∵ sin2A + cos2A= 1)
Hence proved.

Question 3.

If m = a sec A +b tan A and n=atanA + bsecA, then prove that: m2-n2 = a2-b2

Answer 3

m = asec A + btan A         ……(i)
n = a tan A + b sec A       …..(ii)
squaring (i) and (ii)
m2 = a2 sec2 A + b2 tan2 A + 2ab sec A tan A
n2 = a2 tan2 A + b2 sec2 A + 2 ab tan A sec A
Subtracting, we get
m2 – n2 = a2 (sec2 A – tan2 A) + b2 (tan2 A – sec2 A)
= a2x 1 +b2(-1) = a2-b( ∵ sec2A-tan2A= 1)  .
Henceproved

Question 4.

If x = r sin A cos B, y = r sin A sin B and z = r cos A, then prove that: x2 + y2 + z2 = r.

Answer 4

x = r sin A cos B      ….(i)
y = r sin A sin B      ….(ii)
z = r cosA               …….(iii)
Squaring, (i), (ii) & (iii)
x2=r2 sin2 A cos2 B,
y2 = r2sin2Asin2B,
z2 = r2cos2A
Adding, we get,
x2+y2 + z2=r2 (sin2A cos2E + sin2 A sin2 B+cos2A)
= r[sin2A (cos2 B + sin2B) + cos2A]
and = r [sin2 A x 1 + cos2 A]
so = r2 [sin2 A + cos2 A] = r2 x 1  = r2        ( ∵ sin2 A + cos2 A = 1)
Hence proved.

Question 5.

If sin A + cos A = m and sec A + cosec A=n, show that n (m2-1) = 2m

Answer 5

Trigonometrical-Identities EX-21 B Ans-5

Question 6.

If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that x2 + y2 + z2 = r2

Answer 6

x = r cosAcosB              ….(i)
y = r cosAsinB             ….(ii)
z = r sinA                 ….(iii)
Squaring (i), (ii), (iii)
x2 = r2 cos2 A cos2 B, y2 = r2 cos2 A sin2B
z2 = r2sin2A
Adding, we get
x2 + y2 + z2 = r2 (cos2 A cos2B + cos2 A sin2 B + sin2 A)
= r2 [cos2 A (cos2 B + sin2B) + sin2 A]
= r2[cos2Ax 1+sin2A]
= r2 (1) = r2    `Hence proved.

Question 7.

…………
Answer 7

Trigonometrical-Identities EX-21 B Ans-7

Chapter-21 Trigonometrical Identities Concise Solutions EXERCISE – 21 (C)

Question 1.

Show that:
(i) tan 10° tan 15° tan 75° tan 80° = 1
(ii) sin 42° sec 48°+cos 42° cosec 48°= 2
(iii) ………

Answer 1

(i)

tan 10° tan 15° tan 75° tan 80°= 1
L.H.S. = tan 10° tan 15° tan 75° tan 80°
= tan (90° – 80°) tan (90° – 75°) tan 75° tan 80°
and = cot 80° cot 75° tan 75° tan 80°
so = tan 80° cot 80° x tan 75° cot 75°
hence = 1 x 1 = 1= R.H.S. (∵ tan A cot A = 1)
(ii)

sin 42° sec 48°+ cos 42° cosec 48°= 2
L.H.S. = sin 42° sec 48°+ cos 42° cosec 48°
= sin 42° sec (90° – 42°) + cos 42° cosec (90° – 42°)
= sin 42° cosec 42°+ cos 42° sec 42°
=1 + 1=2 R.H.S. (∵ sin A cosec A=1, cos A sec A=1)

Trigonometrical-Identities EX-21C Ans-1 iii

Question 2.

Express each of the following in terms of angles between 0°and 45°.
(i) sin 59° + tan 63°
(ii) cosec 68° + cot 72°
(iii) cos 74° + sec 67°

Answer 2

(i)

sin 59° + tan 63°
= sin (90° – 31°) + tan (90° – 27°)
= cos 31°+ cot 27°
(ii)

cosec 68° + cot 72°
= cosec (90° – 22°) + cot (90° – 18°)
= sec 22°+ tan 18°
(iii)

cos 74°+ sec 67°
= cos (90° – 16°) + sec (90° – 23°)
= sin 16°+ cosec 23°

Question 3.

Show that:
…………

Answer 3

Trigonometrical-Identities EX-21C Ans-3

Question 4.

For triangle ABC, Show that:

Answer 4

Trigonometrical-Identities EX-21C Ans-4

Question 5.

Evaluate:

(i)…

(ii)…….

(iii)………

(iv)………

(v)………

(vi)……..

(vii)…….

(viii)…….

(ix)……….

Answer 5

(i)

Trigonometrical-Identities EX-21C Ans-5 i

Trigonometrical-Identities EX-21C Ans-5 ii

Trigonometrical-Identities EX-21C Ans-5 iii to vii

Trigonometrical-Identities EX-21C Ans-5 viii to iv

Question 6.

………..

Answer 6

Trigonometrical-Identities EX-21C Ans-6

Question 7.

Find (in each case, given below) the value of x, if:
(i) sin x = sin 60° cos 30° – cos 60° sin 30°
(ii) sin x = sin 60° cos 30° + cos 60° sin 30°
(iii) cos x = cos 60° cos 30° – sin 60° sin 30°
(iv) ………….
(v) sin 2x = 2 sin 45° cos 45° 
(vi) sin 3x = 2 sin 30° cos 30°
(vii) cos (2x – 6°) = cos2 30° – cos2 60°

Answer 7

Trigonometrical-Identities EX-21C Ans-7 i to v

Selina Solutions Exe 1 C Chemistry Ans

Trigonometrical-Identities EX-21C Ans-7 vi to vii

Question 8.

In each case, given below, find the value of angle A, where 0° ≤ A ≤ 90°.
(i) sin (90° – 3A). cosec 42° = 1
(ii) cos (90° – A). sec 77° = 1

Answer 8

Trigonometrical-Identities EX-21C Ans-8

Question 9.

Prove that:

…………….

Answer 9

Trigonometrical-Identities EX-21C Ans-9

Question 10.

Evaluate:

………….

Answer 10

Trigonometrical-Identities EX-21C Ans-10

Question 11.

Without using trigonometric tables, evaluate sin2 34° + sin2 56° + 2 tan 18° tan 72° – cot30°.

Answer 11

Trigonometrical-Identities EX-21C Ans-11

Question 12.

Without using trigonometrical tables, evaluate: cosec2 57° – tan2 33° + cos 44° cosec 46° –  \sqrt{2}  cos45°- tan2 60°

Answer 12

Trigonometrical-Identities EX-21C Ans-12

Selina Publishers Concise Maths Solutions of EXERCISE – 21 (D)Trigonometrical Identities 

Question 1.

Use tables to find sine of:
(i) 21°
(ii) 34°42′
(iii) 47° 32′                    
(iv) 62°57′
(v) 10°20′ + 20° 45′

Answer 1

From tables of sine of angles, we find that:
(i)

sin 21°= 0.3584,
(ii)

sin 34°42’= .5693
(iii)

sin 47° 32′ = 0.7377
(iv)

sin 62° 57′ = 0.8906
(v)

sin 10° 20′ + 20°45′ = sin 31°5′
= 0.5162

Question 2.

Use tables to find cosine of:
(i) 2°4′
(ii) 8°12′
(iii) 26°32’                     
(iv) 65°41′
(v) 9°23′ +15°54′

Answer 2

From tables of cosine of angle, we find that:
(i)

cos 2°4′ = 0.9993
(ii)

cos 8° 12’ = 0.9898
(iii)

cos 26°32′ = 0.8946
(iv)

cos 65°41′ = 0.4118
(v)

 cos 9°23′ + 15°54′ = cos 25° 17′
= 0.9042

Question 3.

Use trigonometrical tables to find tangent of:
(i) 37°
(ii) 42°18′
(iii) 17°27′

Answer 3

From the tables of tangents, we find that
(i)

tan 35° = 0.7536
(ii)

tan 42°18’= 0.9099
(iii)

tan 17°27’= 0.3144

Question 4.

Use tables to find the acute angle θ, if the value of sin θ
(i) 4848
(ii) 0.3827
(iii) 0.6525

Answer 4

From the tables of series, we find that of :
(i)

sinθ = 0.4848, then θ = 29°
(ii)

sinθ = 0.3827, then θ = 20° 30′
(iii)

sin θ = 0.6525, then θ = 40° 42’ + 2′ = 40°44′

Question 5.

Use tables to find the acute angle θ, if the value of cos θ is :
(i) 0.9848
(ii) 0.9574
(iii) 0.6885

Answer 5

From the tables of cosines, we find that if :
(i)

cos θ = 0.9848, then θ = 10°
(ii)

cos θ = 0.9574, then θ = 16°48′- 1’=16°47’
(iii)

cos θ = 0.6885, then θ = 46° 30′ or 46°30′
= 46° 29’

Question 6.

Use tables to find the acute angle θ, if the value of tan θ is :
(i) 2419
(ii) 0.4741
(iii) 0.7391                     
(iv) 1.06

Answer 6

From the table of tangents, we find that if:
(i)

tan θ = 0.2419, then θ=13° 36’
(ii)

tan θ = 0.4741, then θ = 25° 18’ + 4’ = 25°22′
(iii)

tan θ = 0.7391, then θ= 36°24’+ 4′ = 36°28′
(iv)

tan θ = 1.06, then θ = 46°36′ + 4′ = 46°40′

Question 7.

If sin θ=0.857; find:
(i) θ                              
(ii) tan θ

Answer 7

From the tables of T. Ratio’s we find this :
(i)

If sin θ = 0.857, then θ = 58°54′ + 4.5′ = 58° 58′ or 58°59’
(ii)

tan 58°58’= 1.6577 +43 = 1.662 or tan 58° 59′ = 1.6577 + 53 = 1.663

Question 8.

If θ is the acute angle and cos θ = 0.7258; find:
(i) θ
(ii) 2 tan θ – sin θ

Answer 8

From the tables of T-ratio’s, we find that:
(i)

If cos θ = 0.7258, then θ= 43° 30′ -2′ = 43°28’
(ii)

Now 2 tan θ – sin θ= 2 tan 43°28′ – sin 43°28′
2 tan 43°28’ = 2 x (0.9457 + 0.0022)
= 0:9479 x 2 = 1.8958
and sin 43°28′ = 0.6871 + 0.0008 = 0.6879
∴ 2 tan 43°28′ – sin 43° 28′ = 1.8958 – 0.6879 = 1.2079

Question 9.

Let θ be an acute angle and tan θ = 0.9490 find:
(i) θ
(ii) cos θ
(iii) sin θ – cos θ

Answer 9

From the tables of T-raios, we find that:
(i)

if tan θ = 0.9490 , then θ = 43°30′
(ii)

cos θ = cos 43°30′ = 0.7254
(iii)

sin θ = sin 43°50′ = 0.6884
∴ sin θ – cos θ = 0.6884 – 0.7254 = -0.0370 = -0.037

 Concise Selina Maths Solutions EXERCISE  – 21 (E)Trigonometrical Identities 

 

Question 1.

Prove the following identities :

(i)…

(ii)…….

(iii)………

(iv)………

(v)………

(vi)……..

(vii)…….

(viii)…….

(ix)………

 (x)……….

(xi)……….

(xii)……….

(xiii)……….

(xiv)……….

(xv)……….

(xvi)……….

(xvii)……….

Answer :1

Answer (i)

Trigonometrical-Identities EX-21D Ans-1 i

Answer :(ii)

Trigonometrical-Identities EX-21E Ans-1 ii

Answer :(iii)

Trigonometrical-Identities EX-21E Ans-1 iii

Answer :(iv)

Trigonometrical-Identities EX-21E Ans-1 iv

Answer :(v)

Trigonometrical-Identities EX-21E Ans-1v

Trigonometrical-Identities EX-21E Ans-1vi

Answer :(vii)

Trigonometrical-Identities EX-21E Ans-1vi

Answer :(viii)

Trigonometrical-Identities EX-21E Ans-1 viii

Answer :(ix)

Trigonometrical-Identities EX-21E Ans-1 ix

Answer :(x)

Trigonometrical-Identities EX-21E Ans-1 x

Answer :(xi)

Trigonometrical-Identities EX-21E Ans-1 xi

Answer :(xii)

Trigonometrical-Identities EX-21E Ans-1 xii

Answer :(xiii)

Trigonometrical-Identities EX-21E Ans-1 xiii

Answer :(xiv)

Trigonometrical-Identities EX-21E Ans-1 xiv

Answer :(xv)

Trigonometrical-Identities EX-21E Ans-1 xv

Answer :(xvi)

Trigonometrical-Identities EX-21 E Ans-1 xvi

Answer (xvii)

Trigonometrical-Identities EX-21E Ans-1 xvii

Question 2.

If sin A + cos A = p and sec A + cosec A = q then prove that: q(p² – 1) 2p

Answer 2

Trigonometrical-Identities EX-21 E Ans-2

Question 3.

………….

Answer 3

Trigonometrical-Identities EX-21 E Ans-3

Question 4.

…………

Answer 4

Trigonometrical-Identities EX-21 E Ans-4

Question 5.

If tan A=n tan B and sin A=m sin B, prove that:

………

Answer 5

Trigonometrical-Identities EX-21 E Ans-5

Question 6.

(i) If 2 sin A-1 = 0, show that:
sin 3 A = 3 sin A – 4 sin3 A.             [2001]
(ii) If 4cos2 A-3 = 0, show that:
cos 3A = 4 cos3 A – 3 cos A

Answer 6

Trigonometrical-Identities EX-21 E Ans-6

Question 7.

Evaluate:

(i)……

(ii)…….

(iii)………

(iv)………

(v)………

(vi)……..

(vii)…..

Answer 7

Trigonometrical-Identities EX-21 E Ans-7 i to iii

Trigonometrical-Identities EX-21 E Ans-7 iv to vii

Question 8.

Prove that:

(i)……

(ii)…….

(iii)………

(iv)………

(v)………

Answer 8

Trigonometrical-Identities EX-21 E Ans-8

Question 9.

If A and B are complementary angles, prove that:
(i) cot B + cos B sec A cos B (1 + sin B)
(ii) cot A cot B – sin A cos B – cos sin B = 0
(iii) cosec2 A + cosec2 B = cosec2 A cosec2 B

 (iv) ………..

Answer 9

Trigonometrical-Identities EX-21 E Ans-9 i to iii

Trigonometrical-Identities EX-21 E Ans-9 iv

Question 10.

Prove that:

(i)…

(ii)…….

(iii)………

(iv)………

(v)………

(vi)……..

(vii)…….

(viii)…….

(ix)………

 (x)……….

Answer 10

Trigonometrical-Identities EX-21 E Ans-10 i, ii

Trigonometrical-Identities EX-21 E Ans-10 iii,iv

Trigonometrical-Identities EX-21 E Ans-10v , vi

Trigonometrical-Identities EX-21 E Ans-10vii , viii

Trigonometrical-Identities EX-21 E Ans-10vii , viii

(x)

Trigonometrical-Identities EX-21 E Ans-10 x

Question 11.

If 4 cos2 A – 3 = 0 and 0° ≤ A ≤ 90°, then prove that : 
(i) sin 3A = 3 sinA – 4 sin3A
(ii) cos 3A = 4 cos3 A – 3 cos A

Answer 11

Trigonometrical-Identities EX-21 E Ans-11 

Question 12.

Find A, if 0° ≤ A ≤ 90° and :
(i) 2 cos2 A – 1 = 0
(ii) sin 3A – 1 = 0
(iii) 4 sin2 A – 3 = 0
(iv) cos2 A – cos A = 0
(v) 2cos2 A + cos A – 1 = 0

Answer 12

Trigonometrical-Identities EX-21 E Ans-12 i to iv

Trigonometrical-Identities EX-21 E Ans-12 v

Question 13.

If 0° < A < 90° ; find A, if :

………

Answer 13

Trigonometrical-Identities EX-21 E Ans-13 i

Trigonometrical-Identities EX-21 E Ans-13 ii

Question 14.

Prove that : (cosec A – sin A) (sec A – cos A) sec2 A = tan A. (2011)

Answer 14

Trigonometrical-Identities EX-21 E Ans-14

Question 15.

Prove the identity : (sin θ + cos θ) (tan θ + cot θ) = sec θ + cosec θ. (2014)

Answer 15

Trigonometrical-Identities EX-21 E Ans-15

Question 16

Evaluate without using trigonometric tables,

sin2 28° + sin2 62° + tan2 38° – cot2 52° + sec2 30°

Answer 16

sin2 28° + sin2 62° + tan2 38° – cot2 52° + sec2 30° 

= sin2 28° + [sin (90 – 28)°]2 + tan2 38° – [cot(90 – 38)°]2 + sec2 30°

= sin2 28°  + cos2 28° + tan2 38° – tan2 38° + sec2 30°

Trigonometrical-Identities EX-21 E Ans-16

 End of Trigonometrical Identities Concise Solutions Chapter-21

Chapter Wise Concise Maths Solutions for ICSE Class 10th Selina Publications 

  1. GST ( Goods and Services Tax)
  2. Banking
  3. Shares and Dividends
  4. Linear In equations in One Variable
  5. Quadratic Equations 
  6. Solving Simple Problems (Based on Quadratic Equations)
  7. Ratio and Proportion ( Including Properties and Uses )
  8. Reminder and Factor Theorems
  9. Matrices
  10. Arithmetic Progression
  11. Geometric Progression
  12. Reflection
  13. Section And Mid Point Formula 
  14. Equation of a Line
  15. Similarity (With Applications to Maps and Models )
  16. Loci (Locus and its Constructions)
  17. Circles
  18. Tangents and Intersecting Chords
  19. Constructions ( Circles)
  20. Cylinder, Cone and Spheres (Surface Area and Volume )
  21. Trigonometrical Identities(Currently Open )
  22. Heights and Distances
  23. Graphical Representation (Histograms and Ogives)
  24. Measures of Central Tendency (Mean , Median, Quartiles and Mode)
  25. Probability

 

Other Subject Chapter-Wise Solutions for ICSE Class 10

 

 

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