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View Full Version : How do you prove this identity?


ellenegaudet
Jan 11, 2011, 06:00 PM
(tan^4x)-(tan^2x)(sec^2x) = -tan^2x

Unknown008
Jan 11, 2011, 10:07 PM
You can do it in a very simple way starting by factoring tan^2x.

\tan^4x - \tan^2x \sec^2x = \tan^2x \tan^2x - \tan^2x \sec^2x

=\tan^2x(\tan^2x - \sec^2x)

Then, recall the pythagoras' identify:

\cos^2x + \sin^2x = 1

Divide this by cos^2x to give:

1 + \tan^2x = \sec^2x

This means that \tan^2x - \sec^2x = -1

Substitute that in

=\tan^2x(\tan^2x - \sec^2x)

What do you get? :)