A math problem on trig identities:?

Question

Prove the following identity:

(1+sinx+cosx)/(1-sinx+cosx) = (1+sinx)/(cosx)

Answer 1

Multiply both sides by both denominators.

And use the famous expansion of 1, namely 1 = sin^2 + cos^2.

You'll be done quickly!

Answer 2

2 cot 2x = 2 cos 2x / sin 2x = = 2[ cos(x)^2 - sin(x)^2)] / [2 sin(x) cos (x)] = = cos(x)^2/[sin(x)cos(x)] - sin(x)^2/[sin(x)cos(x)] = = cos x/ sin x - sin x/cos x = cot x - tan x