Verify the Identity (cot(x)^2)/(csc(x))=csc(x)-sin(x)

Math
Start on the left side.
Apply Pythagorean identity in reverse.
Convert to sines and cosines.
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Apply the reciprocal identity to .
Apply the reciprocal identity to .
Apply the product rule to .
Simplify.
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Multiply the numerator by the reciprocal of the denominator.
One to any power is one.
Apply the distributive property.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Rewrite as .
Rewrite as .
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
Verify the Identity (cot(x)^2)/(csc(x))=csc(x)-sin(x)

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