half angle formulae question

**Stuck Man** · July 18th 2010, 08:55 AM

How do I prove that ( (1-cos A) / (1+cos A) ) = (tan (A/2))^2 ?

I have tried using the half angle formulae for cos A but have not entirely finished the question.

**skeeter** · July 18th 2010, 09:01 AM

Originally Posted by Stuck Man

How do I prove that ( (1-cos A) / (1+cos A) ) = (tan (A/2))^2 ?

I have tried using the half angle formulae for cos A but have not entirely finished the question.

$\displaystyle \tan^2\left(\frac{A}{2}\right) = \frac{\sin^2\left(\frac{A}{2}\right)}{\cos^2\left( \frac{A}{2}\right)} = \frac{\frac{1-\cos{A}}{2}}{\frac{1+\cos{A}}{2}} = \frac{1-\cos{A}}{1+\cos{A}}$

**Stuck Man** · July 18th 2010, 09:13 AM

Thats much shorter than I expected. I used the 'little t' formula for cos A. Thanks.

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