Start on the left side.

Apply pythagorean identity.

Apply the reciprocal identity to .

Write in sines and cosines using the quotient identity.

Apply the product rule to .

Apply the product rule to .

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Combine and .

One to any power is one.

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 (sec(x)^2)/(sec(x)^2-1)=csc(x)^2