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!