# Trigonometric identity proof problem

My problem is from Israel Gelfand's Trigonometry textbook.

Page 48. Exercise 5: d) $\frac{\sin\alpha}{1+\cos\alpha}=\frac{1-\cos\alpha}{\sin\alpha}$

I would appreciate some hints on how to approach the problem.

• Do you know about using "conjugate factors"? – colormegone Jul 10 '14 at 16:40

Hint: Note that $\sin^2\alpha = 1 - \cos^2\alpha$ and the latter expression is a difference of two squares.
• On the right side, multiply by $\frac{1 + \cos \alpha}{1 + \cos \alpha}$. – steven gregory Feb 28 '16 at 8:23