Question

Prove that: $\sqrt{2(1-cos\theta )}=2\sin \frac{\theta }{2}$

Answer 1

$\begin{array}{c}since\\ 1-cos2\theta =2si{n}^2\theta \\ or,1-cos\theta =2si{n}^2\frac{\theta }{2}\\ \sqrt{2(1-cos\theta )}=\sqrt{2\times 2si{n}^2\frac{\theta }{2}}=2\sin \frac{\theta }{2}\end{array}$