Question

How to verify (1-tan^2)/(1+tan^2)=1-2sin^2X?

`(1-tan^2)/(1+tan^2)=1-2sin^2X`
On the LHS I broke it down to `(cos^2-sin^2)/(cos^2+sin^2)` but I am not sure what I should do next.

Answer 1

See below

Explanation:

You're correct about the left hand side . Now recall that `sin^2x + cos^2x = 1`. As a result we're left with:

`cos^2x- sin^2x = 1 - 2sin^2x`

Now we can rewrite `cos^2x` as `1 -sin^2x`.

`1 - sin^2x - sin^2x =1 - 2sin^2x`

`1 - 2sin^2x = 1 - 2sin^2x`

`LHS = RHS`

Hopefully this helps!