Question

The value of 2 sin 5π/12 cos π/12 will be:

(A) 1

(B) √3/2

(C) √3/2 - 1

(D) √3/2 + 1

Answer 1

Answer is (D) √3/2 + 1

2 sin 5π/12  cos π/12

= 2 sin 75° cos 15°

= 2 sin (90° – 15°) cos 15°

= 2 cos 15° cos 15°

= 2 cos² 15°

= cos² × 15° + 1

= cos 30° + 1

= √3/2 + 1