sin2x/1+cos2x = options are: cotx, tanx, secx, cscx

The given expression is sin2x/(1+cos2x).

We can use the double angle identities sin2x = 2sinxcosx and cos2x = 2cos^2x - 1 or cos2x = 1 - 2sin^2x to simplify the expression.

Let's use the identity cos2x = 1 - 2sin^2x.

Substitute cos2x in the expression, we get sin2x/(1 + 1 - 2sin^2x) = sin2x/(2 - 2sin^2x).

Simplify the expression, we get (2sinxcosx)/(2(1 - sin^2x)) = sinxcosx/(1 - sin^2x).

We know that 1 - sin^2x = cos^2x, so substitute it in the expression, we get sinxcosx/cos^2x = sinx/cosx = tanx.

So, the answer is tanx.