Question

Verify the following identity

2 tan x/1+tan^2 x = sin 2x

Answer 1

One of the variations of sin^x + cos^x = 1 is

1 + tan^2x = sec^2x

so
LS = [2(sinx/cosx)]/sec^2x
= (2sinx/cosx)(1/cos^2x)
= 2sinxcosx
= sin 2x
= RS