show that: (1-tanx)/(1+tanx)= (1-sinx)/(cos2x)

Answer 1

Is the denominator on the right cos(2x) or cos^2x ? Neither seems to work.

If x = pi/4, the left side is 0 and the right side is 0.293/0 = infinity, if the denominator is cos 2x.

Therefore what you wrote is not an identity.