Question

Find the value of $\sin \left(\frac{1}{4}{\sin }^{-1}\frac{\sqrt{6}3}{8}\right)$

Answer 1

$\sin \left(\frac{1}{4}{\sin }^{-1}\frac{\sqrt{6}3}{8}\right)$

Let $\frac{1}{4}{\sin }^{-1}\frac{\sqrt{6}3}{8}=\theta$

$\Rightarrow \sin 4\theta =\frac{\sqrt{6}3}{8}=2\sin 2\theta$