Verify identities

Question

tan²x =  sin²x

1+tan²x

Answer 1

  Tan ² X           =        Sin ² X

  1 + Tan ² X

 

 Sin ² X / Cos ²X    

  1    + Sin ²X / Cos²X

 

  Sin ² X / Cos² X                  

( Cos ² X + Sin²X )/ Cos ²X

 

 

  Sin² X        = Sin² X

    1

Answer 2

tan^2(x)/(1+tan^2(x)) =? sin^2(x)
(sin^2(x)/cos^2(x))/(1+sin^2(x)/cos^2(x)) =? sin^2(x)
sin^2(x)/(cos^2(x)+sin^2(x)) =? sin^2(x)
sin^2(x)/(1) = sin^2(x) √