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.

  • $\begingroup$ Do you know about using "conjugate factors"? $\endgroup$ – 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.

  • $\begingroup$ Yes, I saw that, but could not progress, I will try it again and tell you my result. Thank you. $\endgroup$ – George Apriashvili Jul 10 '14 at 16:31
  • $\begingroup$ I got the answer, thank you, looks like I just needed to follow my guess, instead of giving it up. $\endgroup$ – George Apriashvili Jul 10 '14 at 16:53
  • $\begingroup$ On the right side, multiply by $\frac{1 + \cos \alpha}{1 + \cos \alpha}$. $\endgroup$ – steven gregory Feb 28 '16 at 8:23

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