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? :)