Question

If $x={30}^{\circ }$, verify that :

$\sin x=\sqrt{\frac{1-\cos 2x}{2}}$

Answer 1

$x={30}^{\circ }\Rightarrow 2x={60}^{\circ }$
$\therefore \sqrt{\frac{1-cos2x}{2}}=\sqrt{\frac{1-cos60}{2}}=\sqrt{\frac{1-\frac{1}{2}}{2}}=\sqrt{\frac{1}{4}}=\frac{1}{2}$

and

sin x = sin ${30}^{\circ }=\frac{1}{2}$

$\therefore sinx=\sqrt{\frac{1-cos2x}{2}}$