Question

Prove:

(1 - tan²x)/(1 + tan²x) = 1 - 2sin²x

Answer 1

replace the first 1 with sin^2x+cos^2x, this should make proving easier.

Answer 2

@zordoloom, anymore insight you can offer? I've changed 1 + tan²x with sec²x, but I'm unsure if that's a step in the right direction.

Once I get that, I change sec²x to 1/cos²x.
That comes out to be:

[(sin²x + cos²x) - tan²x]/(1/cos²x)

What next?

Answer 3

ok

Answer 4

change the den to sec^2x

Answer 5

then change sec^2x to 1/cos^2x

Answer 6

You should now have (1-tan^2x)/(1/cos^2x)

Answer 7

now change 1-tan^2x to cos^2x

Answer 8

now you should have cos^2(x)-sin^2(x).

Answer 9

I'm sorry but I have to go now. I'll be late for my class. Maybe I can help you later.

Answer 10

Thanks for what you've helped me with so far!
I'll see if I can figure it out from here.

Answer 11

simple as that : )

Answer 12

Much appreciated, epsilon!

Answer 13

yw