Is tan2x=sec2x-1 an identity?
Prove the identity :
We know that, sin2x+cos2x=1
Divide the equation by cos2x.
⇒ sin2xcos2x+cos2xcos2x=1cos2x
Since, sinxcosx=tanx,and 1cosx=secx
⇒tan2x+1=sec2x
rearranging the terms,
⇒sec2x-1=tan2x
Hence, tan2x=sec2x-1 is an identity.