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

Start on the left side.
Apply Pythagorean identity in reverse.
Subtract from .
Because the two sides have been shown to be equivalent, the equation is an identity.
is an identity
Verify the Identity sin(x)^2-cos(x)^2=1-2cos(x)^2