Help with verifying double angle identities (Trigonometry)?

Question

The problem you need to verify is:

sin2x = (2tanx)/(1+tan²x)

You must use double angle identities to verify this. Pathagorean identites may also be used.

*Please not that the perenthesis are just there so you can tell what is on the bottom and what is on the top of the fraction.

Answer 1

sin2x = 2sinxcosx

divide by cos^2x

(2sinxcosx/cos^2x)/ (1/cos^2x)

2 tanx / sec^2x = 2tanx/(1+tan^2x)

Answer 2

sin2x = (2tanx)/(1+tan²x)
2sinxcosx = (2sinx/cosx)/(1+sin^2x/cos^2x)
2sinxcosx = (2sinx/cosx)/(1/cos^2x)
2sinxcosx = 2sinxcosx

Answer 3

sin(2x) = 2cos(x)sin(x), the place the two cancels with the two interior the denominator and the sin(x) cancels with between the sin(x) interior the denominator, leaving you with cos(x)/sin(x) = cot(x)