Question

prove (1+sin2x-cos2x)/(1+sin 2x+cos 2x) = tan x

Answer 1

Hello buddy..

sin2x / (1+cos2x) = tanx

We will use trigonometric identities to solve.

We will start from the left side and prove the right side.

==> we know that:

sin2x - 2sinx*cosx

cos2x = 2cos^2 x -1

I will substitute.

==> sin2x / (1+ cos2x) = 2sinx*cosx / (1+ 2cos^2 x -1)

                                      = 2sinx*cosx/ 2cos^2 x

We will reduce similar.

==> sin2x / (1+ cos2x) = sinx/cosx

But we know that tanx = sinx/cosx

==> sin2x / (1+ cos2x) = tanx...........

Hope it helps you buddy

Answer 2

Hope it helps you.
Thank you.