Start on the left side.

Apply Pythagorean identity in reverse.

Apply the reciprocal identity to .

Apply the reciprocal identity to .

Apply the product rule to .

Multiply the numerator by the reciprocal of the denominator.

One to any power is one.

Apply the distributive property.

Cancel the common factor of .

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)