Start on the left side.

Apply the reciprocal identity to .

Write in sines and cosines using the quotient identity.

Combine the numerators over the common denominator.

Multiply the numerator by the reciprocal of the denominator.

Multiply by .

Multiply by .

Combine.

Apply the distributive property.

Multiply by .

Simplify each term.

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.

Factor out of .

Multiply by .

Factor out of .

Factor out of .

Cancel the common factors.

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

is an identity

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