How do you verify the identity $cos^2beta-sin^2beta=1-2sin^2beta$ ?

Question

14101 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-17T18:34:03

see below

Left Hand Side:

Use the identity $sin^2 beta + cos^2 beta = 1$

$cos^2 beta - sin^2 beta = (1-sin^2 beta)- sin^2 beta$

$=1-sin^2 beta -sin^2 beta$

$=1-2 sin^2 beta$

$:.=$ Right Hand Side

How do you verify the identity cos^2beta-sin^2beta=1-2sin^2betacos^2beta-sin^2beta=1-2sin^2beta?