Q. 14.1( 116 Votes )

Prove the following identities

sec4x – sec2x = tan4x + tan2x

Answer :

LHS = sec4x – sec2x


= (sec2x) 2 – sec2x


We know sec2 θ = 1 + tan2 θ.


= (1 + tan2x) 2 – (1 + tan2x)


= 1 + 2tan2x + tan4x – 1 - tan2x


= tan4x + tan2x = RHS


Hence proved.


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