Proof number one:

prove that $\displaystyle \displaystyle \frac{cosx-sinx}{\cos2x} = \frac{cosx+sinx}{1+\sin2x}$

Proof number two:

prove that $\displaystyle \displaystyle \frac{1+tanx}{1-tanx} = \frac{\cos2x}{1-sinx}$

Any help is appreciated!

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- Apr 2nd 2011, 12:16 PMrtbluetwo trig proofs
Proof number one:

prove that $\displaystyle \displaystyle \frac{cosx-sinx}{\cos2x} = \frac{cosx+sinx}{1+\sin2x}$

Proof number two:

prove that $\displaystyle \displaystyle \frac{1+tanx}{1-tanx} = \frac{\cos2x}{1-sinx}$

Any help is appreciated! - Apr 3rd 2011, 01:21 AMDebsta
In Q1, try replacing cos 2x with cos^2 x - sin^2 x , factorise DOTS and cancel.

Then start with RHS and replace sin 2x with 2 sinx cos x and think about what you could replace the 1 with.

In Q2,

get both sides in terms of sin x and cos x only