Question

How do you prove that (1-cot^2x)/(1+cot^2x)=sin^2x-cos^2x

Answer 1

cot x = cos x / sin x. So substitute that in everywhere, squaring it where it's needed.

Now you can do some algebra on the top and bottom of the fraction.

You'll then need to know that sin^2 x + cos^2 x = 1. You should then have the result.

Answer 2

These sorts of trigonometric identity questions usually just involve algebraic manipulation and knowing some other trigonometric identities.

Answer 3

Yes they do. I seem to often get stuck knowing where to start. I got this one with your help! Thanks.