# Verify the Identity (1-tan(x)^2)/(1+tan(x)^2)=cos(x)^2-sin(x)^2

Start on the left side.
Apply Pythagorean identity.
Rearrange terms.
Apply pythagorean identity.
Convert to sines and cosines.
Write in sines and cosines using the quotient identity.
Apply the reciprocal identity to .
Apply the product rule to .
Apply the product rule to .
Simplify.
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