Quote:

Originally Posted by **Pyotr**

I am completely and utterly stuck on this one problem:

http://img72.imageshack.us/img72/252...846541acb8.png
I am supposed to verify this identity using only the fundamental identities. Could somebody at least lead me in the right way to start this? I have no clue where to even begin with this one :(

Here we go:

$\displaystyle

\frac{\sin(x)}{1+\cos(x)}+\frac{1+\cos(x)}{\sin(x) }=\frac{(\sin(x))^2+(1+cos(x))^2}{(1+\cos(x))\sin( x)}

$

$\displaystyle

=\frac{(\sin(x))^2+1+2\cos(x)+(cos(x))^2}{(1+\cos( x))\sin(x)}=$$\displaystyle \frac{\{(\sin(x))^2+(cos(x))^2\}+1+2\cos(x)}{(1+\c os(x))\sin(x)}

$

$\displaystyle

=\frac{2+2\cos(x)}{(1+\cos(x))\sin(x)}=\frac{2}{ \sin (x)}

$