Question

2(1-2 $si{n}^{2}7\theta$) $sin3\theta$ is equal to

• A. $sin17\theta -11\theta$
• B. $sin11\theta -17\theta$
• C. $cos17\theta -cos11\theta$
• D. $cos17\theta +cos11\theta$

Answer 1

The correct option is A

$sin17\theta -11\theta$

We have,

$2(1-2si{n}^{2}7\theta )sin3\theta =2\left(cos14\theta \right)sin3\theta [\because cos2\theta =1-2si{n}^2\theta ]=2sin3\theta cos14\theta =sin17\theta -sin11\theta$

[$because$) 2 sin A cos B = sin (A + B) - sin (A - B)]

$\therefore$ (1 - 2 sin 2 $7\theta$) $sin3\theta$

$=sin17\theta -sin11\theta$