SOLUTION: prove that -sin(x)-cos(x)cot(x)=-csc(x) is an identity

Question 1201965: prove that -sin(x)-cos(x)cot(x)=-csc(x) is an identity
Found 2 solutions by mananth, Theo:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
prove that -sin(x)-cos(x)cot(x)=-csc(x) is an identity
-sin(x)-cos(x)cot(x)

LCM

....sin^2(x) cancel off

-cosec(x)
PROVED

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
equation is:
-sin(x) - cos(x) * cot(x) = -csc(x)
csc(x) = 1/sin(x)
cot(x) = cos(x) / sin(x)
equation becomes:
-sin(x) - cos(x) * cos(x) / sin(x) = -1/sin(x)
multiply both sides of the equation by sin(x) to get:
-sin^2(x) - cos^2(x) = -1
factor the left side of the equation by -1 to get:
-1 * (sin^2(x) + cos^2(x) = -1
since sin^2(x) + cos^(x) = 1, you get:
-1 = -1.
this confirms the identity is correct.

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