# Help Verifying Identity

• May 6th 2012, 03:13 PM
troe
Help Verifying Identity
Hello everyone. Can someone please help me verify this identity? I am stumped on this one.

csc(x) + cot (x)
______________ = cot (x) csc (x)

tan(x) + sin (x)

Thanks.
• May 6th 2012, 03:57 PM
skeeter
Re: Help Verifying Identity
Quote:

Originally Posted by troe
Hello everyone. Can someone please help me verify this identity? I am stumped on this one.

csc(x) + cot (x)
______________ = cot (x) csc (x)

tan(x) + sin (x)

left side ...

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

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

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

you take it from here ...
• May 6th 2012, 04:39 PM
troe
Re: Help Verifying Identity
The rest of the problem...
Quote:

${\frac{1+cos{x}}{\sin{x}} *} {\frac{cos{x}}{\sin{x}(1+cos{x})} =}{\frac{cos{x}}{\sin{x}} *} {\frac{1}{\sin{x}}} = cotx cscx$
Quick question, how did you arrive at (1+ cosx) in the denominator in the second step?

Thanks
• May 6th 2012, 04:44 PM
skeeter
Re: Help Verifying Identity
Quote:

Originally Posted by troe
The rest of the problem...

Quick question, how did you arrive at (1+ cosx) in the denominator in the second step?

Thanks

factored $\sin{x} + \sin{x}\cos{x}$
• May 6th 2012, 04:52 PM
troe
Re: Help Verifying Identity
Thanks that really help!!!