Q. 154.4( 13 Votes )

Show that tan4 θ +tan2 θ =sec4 θ -sec2 θ.

Answer :

L.H.S: tan4θ + tan2 θ

Taking tan2 θ common, we get


tan2 θ (tan2 θ + 1)


= tan2 θ sec2 θ [ sec2 θ – tan2 θ = 1 tan2 θ + 1 = sec2 θ]


= (sec2 θ – 1) sec2 θ [tan2 θ = sec2 θ – 1]


= sec4 θ – sec2 θ


: R.H.S


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