SOLUTION: prove trigonometric identity (csc^2(x)-1)(sin(x))= cot(x)cos(x)

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Question 604042: prove trigonometric identity (csc^2(x)-1)(sin(x))= cot(x)cos(x)
Answer by lwsshak3(11628) About Me  (Show Source):
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prove trigonometric identity
(csc^2(x)-1)(sin(x))= cot(x)cos(x)
Starting with left side:
(csc^2-1)(sin)
=((1/sin^2)-1)sin
=(1/sin)-sin
=(1-sin^2)/sin
=cos^2/sin
=cos/sin*cos
=cotcos
verified: left side=right side