How do you prove $cos^4theta-sin^4theta=1-2sin^2theta$ ?

Question

14528 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-07T16:03:44

see below

$cos^4 theta-sin^4 theta = 1-2sin^2 theta$

Left Side : $=cos^4 theta-sin^4 theta$

$=(cos^2theta-sin^2theta)(cos^2theta+sin^2theta)$

$=(cos^2theta-sin^2theta)*1$

$=cos^2theta-sin^2theta$

$=1-sin^2theta-sin^2theta$

$=1-2sin^2theta$

$:. =$ Right Side

How do you prove cos^4theta-sin^4theta=1-2sin^2thetacos^4theta-sin^4theta=1-2sin^2theta?