Question

Solve :-

$\sin \left(2{\sin }^{-1}\frac{3}{4}\right)$

Answer 1

$=2\sin \left({\sin }^{-1}\frac{3}{4}\right)\cos \left({\sin }^{-1}\frac{3}{4}\right)$
$=2\cdot \frac{3}{4}\cdot \sqrt{1-{\sin }^2\left({\sin }^{-1}\frac{3}{4}\right)}$
$=2\cdot \frac{3}{4}\cdot \sqrt{1-{\left(\frac{3}{4}\right)}^2}$
$=\frac{3}{2}\sqrt{\frac{7}{16}}$
$=\frac{3\sqrt{7}}{8}$