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

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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