Question

Verify the identity
Cos^2x-Sin^2x=1-2sin^2x

Answer 1

From the basic definitions of sin and cos and the Pythagorean Theorem
cos2(x)+sin2(x)=1

or
cos2(x)=1−sin2(x)

So
cos2(x)−sin2(x)

=(1−sin2(x))−sin2(x)

=1−2sin2(x)

hope this helps.