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.
left side ...
$\displaystyle \frac{\frac{1}{\sin{x}}+\frac{\cos{x}}{\sin{x}}} {\frac{\sin{x}}{\cos{x}} + \frac{\sin{x} \cos{x}}{\cos{x}}}$
$\displaystyle \frac{\frac{1+\cos{x}}{\sin{x}}} {\frac{\sin{x}+\sin{x} \cos{x}}{\cos{x}}}$
$\displaystyle \frac{\frac{1+\cos{x}}{\sin{x}}} {\frac{\sin{x}(1+ \cos{x})}{\cos{x}}}$
you take it from here ...
The rest of the problem...
Quick question, how did you arrive at (1+ cosx) in the denominator in the second step?$\displaystyle {\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 $
Thanks