Who is asking: Student
Level: Secondary

Question:
I can't prove this identity. Can you please help me?
(1-tanx)/(1+tanx)=(1-sin2x)/(cos2x)

Thanks!

Hi,

I wrote everything in terms on sinx and cosx using

tanx = ^sinx/_cosx
sin2x = 2sinx cosx and
cos2x = cos²x - sin²x

The identity then becomes

 ^{cosx - sinx}/_{cosx + sinx} = ^{1 - 2sinx cosx}/_{cos²x - sin²x}

Can you see how to complete it?

Penny

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