Start on the left side.

Apply the reciprocal identity to .

Apply the reciprocal identity to .

Multiply the numerator by the reciprocal of the denominator.

Apply the distributive property.

Multiply by .

Combine and .

Reorder terms.

Rewrite as .

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

is an identity

Verify the Identity (1+csc(x))/(sec(x))=cos(x)+cot(x)