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Trigonometrical Ratios Class-9 Concise ICSE Maths Selina Solutions

Trigonometrical Ratios Class-9 Concise ICSE Mathematics Selina Solutions Chapter-22 .  We provide step by step Solutions of Exercise / lesson-22 Trigonometrical Ratios for ICSE Class-9 Concise Selina Mathematics by R K Bansal.

Our Solutions contain all type Questions with Exe-22 A and Exe-22 B, to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-9 Mathematics .

Trigonometrical Ratios Class-9 Concise ICSE Mathematics Selina Solutions Chapter-22


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 Exe-22 A,

Exe-22 B,

 


Exercise 22 (A), Trigonometrical Ratios Class-9 Concise ICSE Mathematics Selina Solutions

Question 1

From the following figure, find the values of :

(i) sin A

(ii) cos A

(iii) cot A

(iv) sec C

(v) cosec C

(vi) tan C.

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Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-1
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-1-1

Question 2

Form the following figure, find the values of :

(i) cos B

(ii) tan C

(iii) sin2B + cos2B

(iv) sin B. cos C + cos B. sin C

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-2
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-2-1

Question 3

From the following figure, find the values of :

(i) cos A (ii) cosec A

(iii) tan2A – sec2A (iv) sin C

(v) sec C (vi) cot2 C – 1/sin² C

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Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-3
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-3-1

Question 4

From the following figure, find the values of :

(i) sin B (ii) tan C

(iii) sec2 B – tan2B (iv) sin2C + cos2C

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-4
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-4-1

Question 5

Given: sin A = 3/5 , find :

(i) tan A(ii) cos A

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-5

Question 6

From the following figure, find the values of :

(i) sin A

(ii) sec A

(iii) cos2 A + sin2A

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-6

Question 7

Given: cos A = 5/13

Evaluate: (i)( sin A – Cot A ) /2 Tan A (ii) cot A+ (1 / cos A)

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-7
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-7-1

Question 8

Given: sec A =29/11 , evaluate : sin A – 1/ Tan A

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-8
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-8-1

Question 9

Given: tan A =4/3  , find : cosecA/( cot A-sec A)

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-9
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-9-1

Question 10

Given: 4 cot A = 3 find;

(i) sin A

(ii) sec A

(iii) cosec2 A – cot2A.

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-10
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-10-1

Question 11

Given: cos A = 0.6; find all other trigonometrical ratios for angle A.

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-11

Question 12

In a right-angled triangle, it is given that A is an acute angle and tan A =. 5/12

find the value of :

(i) cos A(ii) sin A(iii)  c(os A + sin A) / (cos A – Sin A)

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-12
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-12-1

Question 13

Given: sin θ =p/q

Find cos θ + sin θ in terms of p and q.

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-13
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-13-1

Question 14

If cos A =1/2  and sin B 1/ √2 = , find the value of : .

Tan A – Tan B / ( 1+tan A . Tan B)

Are angles A and B from the same triangle? Explain.

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-14
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-14-1

Question 15

If 5 cot θ = 12, find the value of : Cosec θ + sec  θ

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-15
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-15-1

Question 16

If tan x = 1 1/3, find the value of : 4 sin2x – 3 cos2x + 2

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-16
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-16-1

Question 17

If cosec θ= √5, find the value of:

(i) 2 – sin2  θ- cos2 θ

(ii) ……….

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-17
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-17-1

Question 18

If sec A√2 = , find the value of :…………

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-18
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-18-1

Question 19

If cot = 1; find the value of: 5 tan2 + 2 sin2 – 3

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-19

Question 20

In the following figure:

AD BC, AC = 26 CD = 10, BC = 42,

DAC = x and B = y.

Find the value of :

(i) cot x

(ii) …………

(iii) ………….

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-20
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22a-20-1


Trigonometrical Ratios Class-9 Concise ICSE Mathematics Selina Solutions Exercise 22(B)

Question 1

From the following figure, find:

(i) y (ii) sin xo

(iii) (sec xo – tan xo) (sec xo + tan xo)

 

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-1

Question 2

Use the given figure to find:

(i) sin xo (ii) cos yo

(iii) 3 tan xo – 2 sin yo + 4 cos yo.

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-2
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-2-1

Question 3

In the diagram, given below, triangle ABC is right-angled at B and BD is perpendicular to AC. Find:

(i) cos DBC (ii) cot DBA

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 Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-3

Question 4

In the given figure, triangle ABC is right-angled at B. D is the foot of the perpendicular from B to AC. Given that BC = 3 cm and AB = 4 cm. find:

(i) tan DBC

(ii) sin DBA

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-4
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-4-1

Question 5

In triangle ABC, AB = AC = 15 cm and BC = 18 cm, find cos ABC.

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-5

Question 6

In the figure given below, ABC is an isosceles triangle with BC = 8 cm and AB = AC = 5 cm. Find:

(i) sin B (ii) tan C

(iii) sin2 B + cos2B (iv) tan C – cot B

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-6
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-6-1

Question 7

In triangle ABC; ABC = 90o, CAB = xo, tan xo = and BC = 15 cm. Find the measures of AB and AC.

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-7
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-7-1

Question 8

Using the measurements given in the following figure:

(i) Find the value of sin and tan.

(ii) Write an expression for AD in terms of

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-8

Question 9

In the given figure;

BC = 15 cm and sin B =.

(i) Calculate the measure of AB and AC.

(ii) Now, if tan ADC = 1; calculate the measures of CD and AD.

Also, show that: tan2B – 1/cos² B    = -1

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-9
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-9-1

Question 10

If sin A + cosec A = 2;

Find the value of sin2 A + cosec2 A.

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-10

Question 11

If tan A + cot A = 5;

Find the value of tan2 A + cot2 A.

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-11
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-12

Question 12

Given: 4 sin = 3 cos ; find the value of:

(i) sin (ii) cos

(iii) cot2 – cosec2.

(iv) 4 cos2– 3 sin2+ 2

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-12-1

Question 13

Given : 17 cos = 15;

Find the value of: tan + 2 sec.

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-13
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-13-1

Question 14

Given : 5 cos A – 12 sin A = 0; evaluate  :

………….

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-14

Question 15

In the given figure; C = 90o and D is mid-point of AC. Find

(i)  tan CAB / Tan CDB (ii) Tan ABC / Tan CDB

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-15

Question 16

If 3 cos A = 4 sin A, find the value of :

(i) cos A (ii) 3 – cot2 A + cosec2A.

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-16
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-16-1

Question 17

In triangle ABC, B = 90o and tan A = 0.75. If AC = 30 cm, find the lengths of AB and BC.

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-17
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-17-1

Question 18

In rhombus ABCD, diagonals AC and BD intersect each other at point O.

If cosine of angle CAB is 0.6 and OB = 8 cm, find the lengths of the the side and the diagonals of the rhombus.

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-18
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-18-1

Question 19

In triangle ABC, AB = AC = 15 cm and BC = 18 cm. Find:

(i) cos B (ii) sin C

(iii) tan2 B – sec2 B + 2

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-19
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-19-1

Question 20

In triangle ABC, AD is perpendicular to BC. sin B = 0.8, BD = 9 cm and tan C = 1. Find the length of AB, AD, AC and DC.

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-20
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-20-1

Question 21

Given q tan A = p, find the value of :

…………….

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-21

Question 22

If sin A = cos A, find the value of 2 tan2A – 2 sec2 A + 5.

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-22

Question 23

In rectangle ABCD, diagonal BD = 26 cm and cotangent of angle ABD = 1.5. Find the area and the perimeter of the rectangle ABCD.

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-23
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-23-1

Question 24

If 2 sin x = , evaluate.

(i) 4 sin3 x – 3 sin x.

(ii) 3 cos x – 4 cos3 x.

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-24
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-24-1

Question 25

If sin A = √3/2 and cos B =  √3/2, find the value of : .

………………

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-25
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-25-1

Question 26

Use the information given in the following figure to evaluate:

……………. 6 cot y

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-26
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-26-1

Question 27

If sec A = √2 , find: ………….

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-27
selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-27-1

Question 28

If 5 cos  = 3, evaluate : …………

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-28

Question 29

If cosec A + sin A = 5,1/5 find the value of cosec2A + sin2A.

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-29

Question 30

If 5 cos  = 6 sin ; evaluate:

(i) tan θ (ii) ………..

Answer

selina-icse-solutions-class-9-maths-trigonometrical-ratios-22b-30

 

— End of Trigonometrical Ratios Class-9 Concise Selina Solutions :–


Return to – Concise Selina Maths Solutions for ICSE Class -9

 

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