Question 743460
How do I verify the trigonometric identity? Cotx over 1+cotx^2 = sinxcosx

I took the numerator of the fraction (cotx) and changed it to cosx/sinx and then I took the denominator  (1+cotx^2) and changed it to cscx^2 and then changed it again to 1/sinx^2. So my problem looks like (cosx/sinx)/(1/sinx^2). Is that right? I don't know where to go from there.
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cot/(1+cotx^2) = sinxcosx
cot/csc^2 = sin*cos
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(cos/sin)/(1/sin^2) = sin*cos
cos*sin^2/sin = sin*cos
cos*sin = cos*sin