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**Q.1. Express the trigonometric ratios sin A, sec A and tan A in terms of cot A.****Sol. **From trigonometric identity,

cosec^{2} A - cot^{2} A = 1, we get

cosec^{2} A = 1 + cot^{2}A

â‡’

â‡’

Again from trigonometric identity

sec^{2} A - tan^{2} A = 1

â‡’ sec^{2} A = 1+ tan^{2} A

â‡’

Since **Q.2. Write all the other trigonometric ratios of âˆ A in terms of sec A.****Sol.** Since sin^{2} A+ cos^{2} A = 1,

therefore sin^{2} A = 1 - cos^{2}A

â‡’ **Q.3. Evaluate:**

**(ii) sin 25Â° cos 65Â° + cos 25Â° sin 65Â°****Sol.**

(ii) sin 25Â° cos 65Â° + cos 25Â° sin 65Â°

= sin 25Â° cos (90Â° - 25Â°) + cos 25Â° sin (90Â° -25Â°)

= sin 25Â° sin 25Â° + cos 25Â° cos 25Â°

= sin^{2} 25Â° + cos^{2} 25Â° = 1**Q.4. Choose the correct option. Justify your choice. ****(i) 9 sec ^{2} A âˆ’ 9 tan^{2} A = **

(A) 0

**(A) sec ^{2} A (B) âˆ’1(C) cot^{2} A (D) tan^{2} A**

= 9 x 1 = 9

âˆ´ The option (B) is correct.

(ii) (1 + tan Î¸ + sec Î¸) (1 + cot Î¸ âˆ’ cosec Î¸)

(iii) (sec A + tan A) (1 - sin A)

[Hint: Write the expression in terms of sin Î¸ and cos Î¸]

**[Hint: Simplify LHS and RHS separately]**

** using the identity cosec ^{2} A = 1 + cot^{2} A.**

**(viii) (sin A + cosec A) ^{2} + (cos A + sec A)^{2} = 7 + tan^{2} A + cot^{2} A**

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