SOLUTION: Verify trigonometric identities 1-sinx/1+sinx=sec^2x-2secxtanx+tan^2x

Algebra ->  Trigonometry-basics -> SOLUTION: Verify trigonometric identities 1-sinx/1+sinx=sec^2x-2secxtanx+tan^2x      Log On


   

Question 832149: Verify trigonometric identities
1-sinx/1+sinx=sec^2x-2secxtanx+tan^2x
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Verify trigonometric identities
1-sinx/1+sinx=sec^2x-2secxtanx+tan^2x
***

start with left side:
%281-sin%28x%29%29%2F%281%2Bsin%28x%29%29
%28%281-sin%28x%29%29%2F%281%2Bsin%28x%29%29%29%28%281-sin%28x%29%29%2F%281-sin%28x%29%29%29
%281-2sin%28x%29%2Bsin%5E2%28x%29%29%2F%281-sin%5E2%28x%29%29
%281-2sin%28x%29%2Bsin%5E2%28x%29%29%2F%28cos%5E2%28x%29%29

%28sec%5E2%28x%29%29-%282sin%28x%29%2Fcos%5E2%28x%29%29%2B%28tan%5E2%28x%29%29
sec%5E2%28x%29-2%281%2Fcos%28x%29%29%28sin%28x%29%2Fcos%28x%29%29%2Btan%5E2%28x%29%29
sec%5E2%28x%29-2sec%28x%29tan%28x%29%2Btan%5E2%28x%29
verified: left side=right side