TRIG IDENTITIES QUESTION!

Question

Prove cos2x + sin2x - 1 / cos2x - sin2x + 1 = tanx?

Answer 1

cos2x + sin2x - 1 / cos2x - sin2x + 1 = tanx

given formulas  sin2x = 2sinx cosx

                      cos2x = 2 cosx^2 - 1

                      cos2x = 1- 2 sinx^2

substitute sin2x , cos2x values in the equation

  =(1- 2 sinx^2 + 2sinx cosx -1) / (2 cosx^2 - 1 - 2sinx cosx +1)

 = (-2sinx^2+ 2sinx cosx) /( 2cosx^2 - 2sinx cosx)

take out common signs

=2sinx (-sinx + cosx) / 2cosx(cosx -sinx )

cancel common sings

 =sinx / cosx

 =tanx

to prove the solutions