SOLUTION: Prove that (1-tan^2 x) / (1+tan^2 x) = cos 2 x For each step of the proof I also need to know what rule this applies to (algebra, reciprocal, quotient, Pythagorean, double angl

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Prove that (1-tan^2 x) / (1+tan^2 x) = cos 2 x For each step of the proof I also need to know what rule this applies to (algebra, reciprocal, quotient, Pythagorean, double angl      Log On


   

Question 681990: Prove that (1-tan^2 x) / (1+tan^2 x) = cos 2 x
For each step of the proof I also need to know what rule this applies to (algebra, reciprocal, quotient, Pythagorean, double angle, or sum and differences). Please state the rule after each step

Thank you so so much for your help!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Prove that (1-tan^2 x) / (1+tan^2 x) = cos 2 x
-----
Note: Since sin^2 + cos^2 = 1
Dividing by cos^2 you get: tan^2 + 1 = sec^2
-----
Using that Pythagorean relation you get:
(1-tan^2)/(sec^2) = cos(2x)
------
(1 - (sin^2/cos^2)/sec^2 = cos(2x)
(cos^2-sin^2) = cos(2x)
cos(2x) = cos(2x)