Start on the left side.

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

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.

Combine.

Reorder the factors of .

Combine the numerators over the common denominator.

Simplify each term.

Multiply by .

Multiply by .

Add and .

Subtract from .

Add and .

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.

Now consider the right side of the equation.

Apply the reciprocal identity to .

Apply the product rule to .

One to any power is one.

Combine and .

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

is an identity

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