Start on the left side.

Apply the reciprocal identity to .

Multiply the numerator and denominator of the complex fraction by .

Multiply by .

Combine.

Apply the distributive property.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Simplify the numerator.

Move to the left of .

Rewrite as .

Factor out of .

Factor out of .

Factor out of .

Cancel the common factor of .

Rewrite as .

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

is an identity

Verify the Identity (sec(x)-1)/(1-cos(x))=sec(x)