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

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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