(tan^4x)-(tan^2x)(sec^2x) = -tan^2x
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(tan^4x)-(tan^2x)(sec^2x) = -tan^2x
You can do it in a very simple way starting by factoring tan^2x.
Then, recall the pythagoras' identify:
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Divide this by cos^2x to give:
This means that
Substitute that in
What do you get? :)
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