<s>[INST] Trigonometric equality: $\frac{1 + \sin A - \cos A}{1 + \sin A + \cos A} = \tan \frac{A}{2}$ Can you guys give me a hint on how to proceed with proving this trigonometric equality? I have a feeling I need to use the half angle identity for $\tan \frac{\theta}{2}$. The stuff I have tried so far(multiplying numerator and denominator by $1 + \sin A - \cos A$) has lead to a dead end.

Prove that,
  $$
\dfrac{1 + \sin A - \cos A}{1 + \sin A + \cos A} = \tan \dfrac{A}{2}
$$

 [/INST] First write $A=2b$. Then make appropriate use of $\tan b=\sin b/\cos b$, $\sin2b=2\sin b\cos b$, and $\cos2b=2\cos^2b-1=1-2\sin^2b$. 
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