verify the identity.
cos2 x - sin2 x = 1 - 2sin2 x
the 2's next to the sin and cos on the right sides are powers.
To verify the given identity, cos^2x - sin^2x = 1 - 2sin^2x, we will simplify both sides of the equation separately and show that they are equal.
Starting with the left side of the equation:
cos^2x - sin^2x
We know the Pythagorean identity, sin^2x + cos^2x = 1. Therefore, cos^2x = 1 - sin^2x.
Substituting this value in the original equation, we get:
(1 - sin^2x) - sin^2x = 1 - 2sin^2x
Simplifying further:
1 - sin^2x - sin^2x = 1 - 2sin^2x
1 - 2sin^2x = 1 - 2sin^2x
As both sides of the equation are equal, we have verified that cos^2x - sin^2x = 1 - 2sin^2x.