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$\frac{\sin x}{1+\cos x}=$(choose one option from the followings)

a) $\frac{\sin x}{\cos x}$

b) $\frac{\cos x-1}{\sin x}$

c) $\frac{1-\cos x}{\sin x}$

d) $\frac{\sin x+1}{\cos x}$

From the options, I can see that answer should be c) as by cross-multiplication, we get an identity.

But I am unable to solve it if I don't play with the options.

I wish somebody could help. I am looking for a step-wise-solution approach, staring from the problem and reaching the solution, and not involving the options in the process.

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  • $\begingroup$ math.stackexchange.com/questions/510016/… $\endgroup$ – lab bhattacharjee Oct 2 '13 at 9:26
  • $\begingroup$ Please, try to make the title of your questions more informative. E.g., Why does $a\le b$ imply $a+c\le b+c$? is much more useful for other users than A question about inequality. For more information on choosing a good title, see this post. Also, note the changes I made to your maths expressions, which make them look nicer. $\endgroup$ – Lord_Farin Oct 2 '13 at 9:28
  • $\begingroup$ For this kind of problem, you do need to know options because there are so many more expressions that are equal to the original expression. $\endgroup$ – Tunococ Oct 2 '13 at 9:34
  • $\begingroup$ @Lord_Farin- Points noted for future. Thanks! $\endgroup$ – Ramit Oct 2 '13 at 12:01
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Hint: $$\frac{\sin x}{1+\cos x}=\frac{\sin x(1-\cos x)}{(1+\cos x)(1-\cos x)}.$$

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