SOLUTION: prove the identity: (1-tan'squared'a)/(1+tan'squared'a)= cos'squared'a-sin'squared'a

Algebra ->  Geometry-proofs -> SOLUTION: prove the identity: (1-tan'squared'a)/(1+tan'squared'a)= cos'squared'a-sin'squared'a      Log On


   

Question 477025: prove the identity: (1-tan'squared'a)/(1+tan'squared'a)= cos'squared'a-sin'squared'a
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
prove the identity: (1-tan'squared'a)/(1+tan'squared'a)= cos'squared'a-sin'squared'a
-------------------
(1-tan^2(a))/(1+tan^2(a))
----
(1-(sin/cos)^2)/(1+sin/cos)^2)
----
[(cos^2-sin^2)/cos^2)]/[(cos^2+sin^2)/cos^2)]
-----
Invert the denominator and multiply to get:
[(cos^2-sin^2)/cos^2)]/[cos^2/(cos^2+sin^2)]
---
Cancel the cos^2 factors and convert cos^2+sin^2 to 1 to get:
---
= cos^2-sin^2
Which is the right side of your original problem.
====================
Cheers,
Stan H.
==============