## haleyking345 2 years ago tan^2x - tan^2x sin^2x = sin^2x How in the world could you solve this?

1. TuringTest

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

2. haleyking345

cos^2x

3. TuringTest

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

4. haleyking345

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

5. TuringTest

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

6. haleyking345

tan^2x

7. TuringTest

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

8. TuringTest

use$\tan x=\frac{\sin x}{\cos x}$

9. haleyking345

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

10. TuringTest

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.