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

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