Start on the left side.

Write in sines and cosines using the quotient identity.

Write as a fraction with denominator .

Combine.

Multiply .

Multiply by .

Apply Pythagorean identity in reverse.

Simplify the numerator.

Rewrite as .

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

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

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 cos(x)+sin(x)*tan(x)=sec(x)