Start on the left side.

Apply Pythagorean identity in reverse.

Simplify each term.

Simplify the numerator.

Rewrite as .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Apply the distributive property.

Multiply by .

Subtract from .

Subtract from .

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

is an identity

Verify the Identity 1-(sin(x)^2)/(1-cos(x))=-cos(x)