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

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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