Question

$cos^{2} \alpha - \sin^{2} \alpha = 1 - 2 \sin^{2} \alpha$ How can I prove that? ​

Answer 1

Step-by-step explanation:

We have,

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

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