Start on the left side.

Apply the reciprocal identity to .

Simplify.

Apply the product rule to .

One to any power is one.

Write as a fraction with denominator .

Combine.

Multiply by .

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.

Now consider the right side of the equation.

Apply the reciprocal identity to .

Apply the product rule to .

One to any power is one.

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

is an identity

Verify the Identity 1+sec(x)^2sin(x)^2=sec(x)^2