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Question
Show that tan4θ + tan2θ = sec4θ – sec2θ.
Solution
L.H.S = tan4θ + tan2θ
= tan2θ(tan2θ + 1)
= tan2θ.sec2θ ...[∵ sec2θ = tan2θ + 1]
= (sec2θ – 1).sec2θ ...[∵ tan2θ = sec2θ – 1]
= sec4θ – sec2θ
= R.H.S
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