Question 1054480: 1-tanx/1+tanx = 1-sin2x/cos2x prove
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! Prove that (1-tanx)/(1+tanx) = (1-sin2x)/cos2x
Replace tanx with sinx/cosx:
(1-sinx/cosx)/(1+sinx/cosx)
Multiply numerator and denominator by cosx:
(cosx-sinx)/(cosx+sinx)
Multiply numerator and denominator by cosx-sinx:
(cos^2x-2sinxcosx+sin^2x)/(cos^2x-sin^2x)
For the numerator, since sin2x = 2sinxcosx, and sin^2x + cos^2x = 1, we have 1-sin2x
For the denominator, cos^2x - sin^2x = cos2x
So (1-tanx)/(1+tanx) = (1-sin2x)/cos2x
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