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

Question

4457 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-06T20:49:19

see below

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

Left Side : $=2sin^2 theta cos^2 theta + cos ^4 theta$

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

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

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

$=cos^2 theta (sin^2theta +1)$

$=(1-sin^2 theta)(1+sin^2 theta)$

$=1-sin^4 theta$

$=$ Right Side

How do you prove 2sin^2thetacos^2theta+cos^4theta=1-sin^4theta2sin^2thetacos^2theta+cos^4theta=1-sin^4theta?