How do you verify the identity cos2x-sin2x=1-2sin2x.
Verify the given identity:
Given expression: cos2x-sin2x.
It is known that, cos2(x)+sin2(x)=1
⇒cos2(x)=1-sin2(x).
Substitute cos2(x) with 1-sin2(x) in given expression,
⇒cos2(x)-sin2(x)=1-sin2(x)-sin2(x)⇒cos2(x)-sin2(x)=1-2sin2(x)
Therefore, the given identity, cos2(x)-sin2(x)=1-2sin2(x) is verified.