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Answer on Trigonometry Question for Elizabeth

Question #1509
Verify the identity algebraically sinx+cosx(cotx)=cscx. I need to prove that the left half of the equation in fact equals the right, but I am unsure which trigonometric identity to use to simplify the equation. If it could be shown in step by step how this is done, it would help me greatly as I am unsure of which trig. functions to use.
Expert's answer
sinx + cosx (cot x) = sinx + cosx (cosx / sinx) = (sin2x + cos2x)/sinx= 1/sinx = csc x

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