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**Q.1. Evaluate the following:****(i) sin 60Â° cos 30Â° + sin 30Â° cos 60Â°****(ii) 2 tan ^{2} 45Â° + cos^{2} 30Â° âˆ’ sin^{2} 60Â°**

**Sol.** (i) sin 60Â° cos 30Â° + sin 30Â° cos 60Â°

(ii) 2 tan^{2} 45Â° + cos^{2} 30Â° - sin^{2} 60Â°

numerator and denominator by (1 - âˆš3 )]

On multiplying numerator and denominator by (3âˆš3 - 4) we get**Q.2. Choose the correct option and justify your choice:****(A) sin 60Â° (B) cos 60Â° (C) tan 60Â° (D) sin 30Â°**

(C) sin 45Â°

(D) 0

(B) 30Â°

(C) 45Â°

(D) 60Â°

(B) sin 60Â°

(C) tan 60Â°

(D) sin 30Â°

Correct option is (A)

Correct option is (D)

(Hi) sin 2A = 2 sin A, for A = 0Â°

LHS sin 2 A = sin 2 x 0 = sin 0Â° = 0

RHS 2 sin A = 2 sin 0Â° = 2 x 0 = 0

Correct option is (A)

Correct option is (C)

â‡’ A + B = 60Â° ...(i)

â‡’ A - B = 30Â° ......(ii)

Adding (i) and (ii), we get

2A = 90Â°

â‡’ A = 90Â°/2 = 45Â°

From (i), 45Â° + B = 60Â°

â‡’ B = 60Â° - 45Â° = 15Â°

Hence, âˆ A = 45Â°, âˆ B = 15Â°

Then, LHS = sin(60Â° + 30Â°) = sin 90Â° = 1

and RHS = sin A + sin B - sin 60Â° + sin 30Â°

âˆ´ LHS â‰ RHS (False)

(ii) sin 0Â° = 0,

âˆ´ Value of sin 0 increases as 0 increases (True)

(iii) cos 0Â° = 1,

âˆ´ Value of cos Î¸ decreases as Î¸ increases (False)

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