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 .

Add and .

Add and .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Reorder and .

Rewrite as .

Factor out of .

Factor out of .

Rewrite as .

Apply pythagorean identity.

Move the negative in front of the fraction.

Now consider the right side of the equation.

Apply the reciprocal identity to .

Write in sines and cosines using the quotient identity.

Combine and .

Move the negative in front of the fraction.

Multiply .

Multiply and .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Move to the left of .

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

is an identity

Verify the Identity 1/(cos(x)+1)+1/(cos(x)-1)=-2csc(x)cot(x)