How do you use the trigonometric identity cos2x=cos2x-sin2x to verify that cos2x=2cos2x-1.
Verify the given identity:
Given identity: cos2x=cos2x-sin2x.
It is known that, cos2x+sin2x=1
⇒sin2x=1-cos2x.
Substitute sin2x with 1-cos2x in given identity
⇒cos2x=cos2x-1-cos2x⇒cos2x=cos2x-1+cos2x⇒cos2x=2cos2x-1
Therefore, the given identity, cos2x=2cos2x-1 is verified.