Question

tan^2x - tan^2x sin^2x = sin^2x
How in the world could you solve this?

Answer 1

\[\tan^2x-\tan^2x\sin^2x=\tan^2x(1-\sin^2x)\]and what is the identity for \(1-\sin^2x\) ?

Answer 2

cos^2x

Answer 3

right, so now what do you have on the left?

Answer 4

tan^2x-tan^2xsin^2x=tan^2x

Answer 5

no, I mean after what we just did...

Answer 6

tan^2x

Answer 7

\[\tan^2x-\tan^2x\sin^2x=\tan^2x(1-\sin^2x)=\tan^2x\cos^2x=?\]

Answer 8

use\[\tan x=\frac{\sin x}{\cos x}\]

Answer 9

that would leave you with sin^2x as the answer

Answer 10

which is what you have on the left, which proves the identity
if you want a solution, the answer is \(\mathbb R\), but I think the point here was just to prove the identity.