Class 10 || Maths || Exe || Ch. 08.02 Introduction to Trigonometry

Class 10 || Maths || Exe || Ch. 08.02 Introduction to Trigonometry

Exercise 8.2 

Q. 1. Evaluate the following:

   sin 30° + tan 45°–cosec60°       sec 30° + cos 60° + cot 45°

Sol.

Q. 3.
If tan (A + B) = √3 and tan (A – B) = 1√3; 0° < A + B ≤ 90°; A > B, find A and B.
Solution:

 Ex 8.3 

Question 1.
Evaluate:

Solution:

Question 3.
If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A.
Solution:

Question 5.
If sec 4A = cosec (A – 20°), where 4A is an acute angle, find the value of A.
Solution:

Question 6.
If A, B and C are interior angles of a triangle ABC, then show that: sin (B+C)/2 = cos A/2
Solution:

Question 7.
Express sin 61° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.
Solution:

Ex 8.4 

Question 1.

Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.Solution:

Question 2.
Write all the other trigonometric ratios of ∠A in terms of sec A.
Solution:
 

Question 3.

Evaluate:

Solution:

Question 4.
Choose the correct option. Justify your choice.
(i) 9 sec² A – 9 tan² A = ……
(A) 1                 (B) 9
(C) 8                 (D) 0

(ii) (1 + tan θ + sec θ) (1 + cot θ – cosec θ) = ………..
(A) 0                (B) 1
(C) 2                (D) -1

(iii) (sec A + tan A) (1 – sin A) = ………….
(A) sec A            (B) sin A
(C) cosec A        (D) cos A

(iv) 1+tan2A1+cot2A = ………..
(A) sec² A.          (B) -1
(C) cot² A.           (D) tan² A
Solution:

Question 5.
Prove the following identities, where the angles involved are acute angles for which the expressions are defined.

Solution:

A