These NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.1 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry Exercise 8.1

Question 1.

In ∆ABC right angled at B, AB = 24 cm, BC = 7 cm. Determine:

(i) sin A, cos A

(ii) sin C, cos C

Solution:

We have given that,

∆ABC is a right angle ∆, right angled at B and AB = 24 cm, BC = 7 cm

∴ By Pythagoras theorem

Question 2.

In given figure, find tan P – cot R.

Solution:

We have given that ∆PQR is a right angled A, right angle at Q. and PQ = 12 cm, PR = 13 cm

∴ By Pythagoras theorem, we know that

Question 3.

If sin A = \(\frac { 3 }{ 4 }\), calculate cos A and tan A.

Solution:

Given

Question 4.

Given 15 cot A = 8, find sin A and sec A.

Solution:

Question 5.

Given sec θ = \(\frac { 13 }{ 12 }\) , calculate all other trigonometric ratios.

Solution:

Question 6.

If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.

Solution:

Question 7.

If cot θ = \(\frac { 7 }{ 8 }\), evaluate:

(i) \(\frac { \left( 1+sin\theta \right) \left( 1-sin\theta \right) }{ \left( 1+cos\theta \right) \left( 1-cos\theta \right)}\)

(ii) cot²θ

Solution:

Question 8.

If 3 cot A = 4, check whether \(\frac { 1-tan^{ 2 }A }{ 1+tan^{ 2 }A }\) = cos² A – sin² A or not.

Solution:

Question 9.

In triangle ABC, right angled at B, if tan A = \(\frac { 1 }{ \surd 3 }\), find the value of:

(i) sin A cos C + cos A sin C

(ii) cos A cos C – sin A sin C

Solution:

Question 10.

In ΔPQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.

Solution:

Question 11.

State whether the following statements are true or false. Justify your answer.

(i) The value of tan A is always less than 1.

(ii) sec A = \(\frac { 12 }{ 5 }\) for some value of angle A.

(iii) cos A is the abbreviation used for the cosecant of angle A.

(iv) cot A is the product of cot and A.

(v) sin θ = \(\frac { 4 }{ 3 }\) for some angle.

Solution:

(i) tan 60° = √3 , Since √3 > 1. (False)

(ii) sec A is always ≥ 1. (True)

(iii) cos A is the abbreviation for cosine A. (False)

(iv) cot without ∠A is meaningless. (False)

(v) sin θ can never be greater than 1.

∴ sin θ = \(\frac { P }{ H }\), hypotenuse is always greater than other two sides. (False)