Question

by using formula of cos⁡2θ establish ; sin⁡θ=±√(1-cos⁡2θ )/2

Answer 1

Step-by-step explanation:

We have,

$\cos(2 \theta) = \cos^{2} ( \theta) - \sin^{2} ( \theta)$

$\implies \cos( 2\theta) = 1 - 2 \sin^{2} ( \theta)$

$\implies2 \sin^{2} ( \theta) = 1 - \cos( 2\theta)$

$\implies\sin^{2} ( \theta) = \frac{ 1 - \cos( 2\theta) }{2}$

$\implies\sin ( \theta) = + - \sqrt{ \frac{ 1 - \cos( 2\theta) }{2}}$