Gujarat Board Solutions Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.4

Gujarat Board Solutions Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.4

Gujarat Board Textbook Solutions Class 10 Maths Chapter 8 Introduction to Trigonometry Ex 8.4

Question 1.
Express the trigonometric ratios sin A, sec A and tan A in terms of cot A. (CBSE 2012)
Solution:

(ii) sin 25° cog 65° + cos 25° sin 65°
= sin 25° cos (90° – 25°) + cos 25° sin (90° – 25°)
= sin 25° sin 25° + cos 25° cos 25°
= sin² 25° + cos² 25
= 1

Question 4.
Choose the correct option. Justify your choice.
(i) 9 sec² θ – 9 tan² θ =
(a) 1
(b) 9
(c) 8
(d) 0

(ii) (1 + tan θ + sec θ) (1 + cot θ – cosec θ)=
(a) –
(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

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

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