SOLUTION: Prove the following identities: A) cos2x/cosx+sinx = cosx - sinx B) 1-tan^2(x)/1+tan^2(x) = cos2x

Algebra ->  Trigonometry-basics -> SOLUTION: Prove the following identities: A) cos2x/cosx+sinx = cosx - sinx B) 1-tan^2(x)/1+tan^2(x) = cos2x      Log On


   

Question 1022170: Prove the following identities:
A) cos2x/cosx+sinx = cosx - sinx
B) 1-tan^2(x)/1+tan^2(x) = cos2x
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Prove the following identities:
A) cos2x/cosx+sinx = cosx - sinx
cos(2x) = cos^2(x) - sin^2(x)
QED
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B) 1-tan^2(x)/1+tan^2(x) = cos2x
(1-tan^2(x))*cos^2(x)/(1+tan^2(x))*cos^2(x)) = cos2x
(cos^2(x) - sin^2(x)/(cos^2(x) + sin^2(x)) = cos(2x)
cos^2(x) - sin^2(x) = cos(2x)
QED
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