How do you prove # tan^2xcos^2x=(-cos2x+1)/2 #?

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Answer 1 · 2016-03-06T09:28:27

As both sides are equal to #sin^2x#

As #cos2x=(1-2sin^2x)#, we can write #(-cos2x+1)/2# as

#(-(1-2sin^2x)+1)/2# or

#(-1+2sin^2x+1)/2# or

#2sin^2x/2# or #sin^2x#

Now #tan^2xcos^2x#

#(sin^2x/cancel(cos^2x))xxcancel(cos^2x)#

= #sin^2x#.

Hence #tan^2xcos^2x=(-(1-2sin^2x)+1)/2#