Question

If $x={30}^o$, verify that $\sin x=\sqrt{\frac{1-\cos 2x}{2}}$

Answer 1

$x=30°$

Taking L.H.S.,

$\sin x=\sin 30°=\frac{1}{2}$

Taking R.H.S.,

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

$=\sqrt{\frac{1-\cos (2\cdot 30°)}{2}}$

$=\sqrt{\frac{1-\cos 60°}{2}}$

$=\sqrt{\frac{1-\frac{1}{2}}{2}}$

$=\sqrt{\frac{\frac{1}{2}}{2}}$

$=\sqrt{\frac{1}{4}}$

$=\frac{1}{2}$

$=$ L.H.S.

Hence verified that $\sin x=\sqrt{\frac{1-\cos 2x}{2}}$.