Prove that (sec⁴ teta- sec²teta) = (tan²teta+ tan⁴teta)
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Answer:
Given :
sec⁴ θ – sec²θ = tan⁴θ + tan²θ
L.H.S
= sec⁴ θ – sec²θ
= sec² θ (sec² θ -1)
= (1 + tan² θ) (1 + tan² θ -1) …..[ sec² θ = 1 + tan² θ ]
= (1 + tan² θ) ( tan² θ)
= tan²θ + tan⁴θ
L.H.S = R.H.S
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