SOLUTION: I need help with this trig identity. Prove the identity: cos^2x = 1-cos^2xtan^2 Please show your steps. Thanks

Algebra ->  Trigonometry-basics -> SOLUTION: I need help with this trig identity. Prove the identity: cos^2x = 1-cos^2xtan^2 Please show your steps. Thanks      Log On


   

Question 671602: I need help with this trig identity.
Prove the identity:
cos^2x = 1-cos^2xtan^2
Please show your steps.
Thanks
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Given
(1) cos^2x = 1 - cos^2x*tan^2x
Use the ID
(2) tanx = sinx/cosx, easily proven.
Then
(3) tan^2x = sin^2x/cos^2x
Substitute (3) into (1) and get
(4) cos^2x = 1 - sin^2x or
(5) sin^2x + cos^2x = 1 another easily proven ID