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Question
Prove the following identities.
tan4 θ + tan2 θ = sec4 θ – sec2 θ
Solution
tan4 θ + tan2 θ = sec4 θ – sec2 θ
L.H.S = tan4 θ + tan2 θ
Taking out tan2 θ as common
= tan2 θ (tan2 θ + 1)
We know that
1 + tan2 θ = sec2 θ
i.e. tan2 θ = sec2 θ - 1
It can be written as
= (sec2 θ – 1) sec2 θ
So we get
= sec4 θ – sec2 θ
= R.H.S
Therefore, it is proved.
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