Start on the left side.

Apply pythagorean identity.

Apply the reciprocal identity to .

Write in sines and cosines using the quotient identity.

Multiply .

Multiply and .

Raise to the power of .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Cancel the common factor of .

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

is an identity

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