Start on the left side.

Multiply by .

Combine.

Apply the distributive property.

Multiply by .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Apply pythagorean identity.

Write in sines and cosines using the quotient identity.

Simplify each term.

Factor out of .

Multiply by .

Factor out of .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Combine the numerators over the common denominator.

Simplify the numerator.

Rewrite as .

Because the two sides have been shown to be equivalent, the equation is an identity.

is an identity

Verify the Identity -cot(t)+(sin(t))/(1-cos(t))=csc(t)