# Power Reduction Formulas/Sine Squared

(Redirected from Square of Sine)

## Theorem

$\sin^2 x = \dfrac {1 - \cos 2 x} 2$

where $\sin$ and $\cos$ denote sine and cosine respectively.

## Proof

 $\ds 1 - 2 \sin^2 x$ $=$ $\ds \cos 2 x$ Double Angle Formula for Cosine: Corollary 2 $\ds \leadsto \ \$ $\ds \sin^2 x$ $=$ $\ds \frac {\cos 2 x - 1} {-2}$ solving for $\sin^2x$ $\ds$ $=$ $\ds \frac {1 - \cos 2 x} 2$ multiplying top and bottom by $-1$ and rearranging terms

$\blacksquare$

## Historical Note

The Square of Sine formula was discovered and documented by Varahamihira in the $6$th century CE.