Start on the left side.

Rearrange terms.

Apply pythagorean identity.

Write in sines and cosines using the quotient identity.

Apply the reciprocal identity to .

Apply the product rule to .

Apply the product rule to .

Multiply the numerator by the reciprocal of the denominator.

One to any power is one.

Divide by .

Apply the distributive property.

Multiply by .

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 (1-tan(x)^2)/(1+tan(x)^2)=cos(x)^2-sin(x)^2