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

Question

$(1-tan^2)/(1+tan^2)=1-2sin^2X$
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.

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Answer 1 · 2018-01-30T21:37:41

See below

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!