Q63 / 160 · AP EAMCET 2019 (21 Apr Shift 2) · Mathematics

If $4 (\sin 2 x \sin 4 x + \sin^{2} x) = 3$ , then $x =$

Solution

Simplify the given expression

$4 (\sin 2 x \sin 4 x + \sin^{2} x) = 3$

$\Rightarrow 2 (\cos 2 x - \cos 6 x) + 2 (1 - \cos 2 x) = 3$

$\Rightarrow 2 \cos 2 x - 2 \cos 6 x + 2 - 2 \cos 2 x = 3$

$\Rightarrow - 2 \cos 6 x + 2 = 3$

$\Rightarrow \cos 6 x = - \frac{1}{2}$

Therefore, $6 x = 2 π n \pm \frac{2 π}{3}$

$\Rightarrow x = \frac{2 n π}{6} \pm \frac{2}{6} \times \frac{π}{3}$

$\Rightarrow x = \frac{n π}{3} \pm \frac{π}{9}$

Hence, the correct answer is option: 'B'.