How do you verify the identity below?

Question

#4cos^2(x)-sin^2(x)=5cos^2(x)-1 #

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Answer 1 · 2018-03-06T15:51:24

See Below

Use the identity
#sin^2x+cos^2x=1#

#sin^2x=1-cos^2x#

LHS: #4cos^2x-sin^2x#

#=4cos^2x-(1-cos^2x)#

#=4cos^2x-1+cos^2x#

#=4cos^2x+cos^x-1#

#=5 cos^2x -1#

=RHS