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Q.

Which is equal to tan4 θ + tan2 θ.

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a

( sec4 θ - sec2 θ)2

b

sec4 θ - sec2 θ

c

( sec4 θ + sec2 θ)2

d

sec4 θ + sec2 θ

answer is B.

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Detailed Solution

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 tan4 θ + tan2 θ= tan2 θ (tan2 θ + 1)

= (sec2 θ - 1) (tan2 θ + 1)      [since, tan2 θ = sec2 θ – 1]

= (sec2 θ - 1) sec2 θ               [since, tan2 θ + 1 = sec2 θ]

= sec4 θ - sec2 θ.

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