Trigonometrical Ratios of Standards Angles ML Aggarwal Class-9

Solutions of Understanding APC Mathematics Exercise-18 with MCQ and Chapter-Test for ICSE Board Class-9

Trigonometrical Ratios of Standards Angles ML Aggarwal ICSE Class-9 Chapter-18 . Step by Step Answer of Exercise-18.1, Exercise-18.2, MCQ and Chapter-Test of  Exercise-18 Trigonometrical Ratios of Standards Angles for ICSE Class-9 Understanding APC Mathematics. Visit official website CISCE for detail information about ICSE Board Class-9.

Trigonometrical Ratios of Standards Angles ML Aggarwal ICSE Class-9


–: Select Topics :–

Exercise-18.1 ,

Exercise-18.2

 MCQ  

Chapter-Test

(before each solutions some part of the questions is also written as hint to avoid confusion)

Note:- Before viewing Solutions of Chapter -18 Trigonometrical Ratios of Standards Angles Class-9 of ML Aggarwal Solutions .  Read the Chapter Carefully then solve all example given in Exercise-18.1, Exercise-18.2. The Chapter-18 Trigonometrical Ratios of Standards Angles Class-9 is Main Chapter in ICSE Mathematics.


Exercise 18.1 Trigonometrical Ratios of Standards Angles ML Aggarwal

Question 1

Find the value of…………..

Answer 1

Question 2

Find the value of…………..

Answer 2

 

 

Question 3

Find the value of…………..

Answer 3

 

 

Question 4

Prove that…………..

Answer 4

 

 

Question 5

(i) if………..

(ii) if…………….

Answer 5

 

Question 6

Find the value of…………..

Answer 6

 

Question 7

if…………..verify that ………….

Answer 7

 

 

Question 8

If 0 = 30°, find the ratio 2 sin 0: sin 2 0.

Answer 8

 

Question 9

By means of an example, show that sin (A + B) + sin A + sin B.

Answer 9

 

Question 10

 If A = 60° and B = 30°, verify that
(i) sin (A + B) = sin A cos B + cos A sin B
(ii) cos (A + B) = cos A cos B- sin A sin B

Answer 10

 

Question 11

…………….sin (A – B) = sin A cos B – cos A sin B
tan A – tan B………………

Answer 11

 

Question 12

 If 0 is an acute angle and sin 0 = cos 0, find the value of 0 and hence, find the value

Answer 12

 

Question 13

 From the adjoining figure, find

Answer 13

 

 

Question 14

 If 30 is an acute angle, solve the following equations for 0:……….

Answer 14

 

 

Question 15

 If tan 3x = sin 45° cos 45° + sin 30°, find the value of x.

Answer 15

 

Question 16

 If 4 cos? x -1 = 0 and 0 sxS 90, find……………

Answer 16

 

Question 17

Answer 17

 

Question 18

Answer 18

 

Question 19

Answer 19

 

Question 20

Answer 20

 

Question 21

Answer 21

 

 

Question 22

If the length of each side of a rhombus is 8 cm and its one angle is 60°, then …..

Answer 22

 

 

Question 23

In the right-angled triangle ABC, 2C = 90° and ZB = 60°. If AC = 6 cm, fr
lengths of the diagonals of the rhombus.
lengths of the sides BC and AB.

Answer 23

 

Question 24

In the adjoining figure, AP is a man of height
1-8 m and BQ is a building 13-8 m high. If the
man sees the top of the building by focussing his
binoculars at an angle of 30° to the horizontal,
find the distance of the man from the building.

Answer 24

 

Question 25

In the adjoining figure, ABC is a triangle in
which ZB = 45° and ZC = 60°., If AD 1 BC and
BC = 8 m, find the length of the altitude AD

Answer 25

 


EXERCISE – 18.2 Understanding APC Solutions 

Question 1

Answer 1

Question 2

Answer 2

 

 

Question 3

 (i)sin 62°-cos 28° (ii) cosec 35° – sec 55°,………..

Answer 3

 

Question 4

 

Answer 4

Question 5

Answer 5

 

 

Question 6

 Express each of the following in terms of trigonometric ratios of angles be
to 45° :…………

Answer 6

 

Question 7

Answer

 

 

Question 8

Answer 8

 

Question 9

Answer 9

 

Question 10

Answer 10

 

Question 11

 

Answer 11

 

 

Question 12

without using trigonometrical tables, evaluate:

Answer 12

 

 

Question 12

Prove the following:

Answer 1

 

Question 14

Prove the following:………..

Answer 14

 

Question 15

Simplify the following :………..

Answer 15

 

Question 16

Show that Cos (45° + 0) + cos²(45° – 0)=1
tan(60° + 0) tan(30° – 0)

Answer 16

 

Question 17

Find the value of A if
(i) sin 3A = cos (A-6°), where 3A and A-6° are acute angles
(ii) tan 2A = cot (A- 18°), where 2A and A- 18° are acute angles.
(tii) If sec 2A = cosec (A – 27°) where 2A is an acute angle, find the measure of ZA

Answer 17

 

 

 

Question 18

Find the value of 0 (0° < 0 < 90°) if :
(i) cos 63° sec (90° – 0) = 1
(ii) tan 35° cot (90° – 0) = 1

Answer 18

 

Question 19

If A, B and C are the interior angles of a AABC, show that

Answer 19

 

 


Multiple Choice Question of Chapter-18 Trigonometrical Ratios of Standards Angles ML Aggarwal (MCQ)

Question 1

the value of ………….

Answer 1

 

Question 2

the value of ………….

Answer 2

Question 3

the value of ………….

Answer

 

Question 4

…………30, then the value of 2 sin A cos A is

Answer 4

 

Question 

The value of 3 cosec 60- sec 60 is…………..

Answer 5

 

Question 6

The value of……………

Answer 6

 

Question 7

The value of…………..

Answer 7

 

Question 8

If tan A 3, then the value of cosec A is………….

Answer 8

 

Question 9

If sec 0.sin e 0, then the value of cos 6 is…………

Answer 9

 

 

Question 10

if…………….

Answer 10

 

Question 11

the value of …………….

Answer 11

 

Question 12

if sin ………………

Answer 12

 

Question 13

If …ABC is right angled at C, then the value of cos (A + B) is…

Answer 13

 

Question 14

In the adjoining figure, ABC is a right triangle right
angled at B. If AB = 10 cm and ZC = 30°, then the
length of the side BC is……….

Answer 14

 

Question 15

In the adjoining figure, PQR is a right triangle right
angled at Q. If PQ = 4 cm and PR = 8 cm then ZP is
equal to………………..

Answer 15

 

 


Chapter Test of Trigonometrical Ratios of Standards Angles 

Question 1

Find the values of……………

Answer 1

 

Question 2

Taking A 30, verlfy that
(i) ……………..
(ii) ……………….

Answer 2

 

 

Question 3

if a =…………..

Answer 3

 

Question 4

Taking A 60° and B 30, verify that

Answer 4

 

 

Question 5

If …………. < 20 < 90°, find the value of

Answer 5

 

Question 6

 If 30 is an acute angle, solve the following equation for ………….

Answer 6

 

Question 7

If tan (A + B) = 13, tan (A – B) = 1 and A, B (B < A) are acute angles, find the………

Answer 7

 

 

 

Question 8

 Without using trigonometrical tables, evaluate the following:

Answer 8

 

 

Question 9

Prove that:

Answer 9

 

Question 10

When 0° < A < 90°, solve the following equations:…………..

Answer 10

Question 11

Find the value of 0 if
(1) sin (0 +36°) = cos 0, where 0 and 0+36° are acute angles.
(ii) sec 40 = cosec (0-20°), where 40 and 0-20° are acute angles.

Answer 11

 

Question 12

In the adjoining figure, ABC is right-angled triangle at B and
ABD is right angled triangle at A. If BD 1 AC and BC = 2 3 cm,
find the length of AD.

Answer 12

 

Return to ML Aggarawal Maths Solutions for ICSE  Class-9.


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