SOLUTION: 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

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. Can you please go step by step so I can see what you did? Thank you.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
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.
=====================
cot/(1+cotx^2) = sinxcosx
cot/csc^2 = sin*cos
---
(cos/sin)/(1/sin^2) = sin*cos
cos*sin^2/sin = sin*cos
cos*sin = cos*sin
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