trig
posted by kelly .
transform the expression on left to one on right
csc xsin x to cot x cos x

csc xsin x = (1/sinx)  sin x
= (1  sin^2 x)/sin x = (cos x * cos x)/sin x
= cos x cot x 
We have trig identities.
cscx  sinx to cotx(cos x).
cscx is the reciprocal of the sine function.
So, then:
cscx = 1/sinx
We now have:
1/sinx  sinx...Treat this like a fraction case.
1/sinx  sinx becomes (1  sin^2x)/sinx
Of course, (1  sin^2x) is one of the Pythagorean Identities, recall?
We know that (1  sin^2x) = cos^2x
We now have:
cos^2x/sinx = the right side
Done!