Question

Change sec⁴ θ -sec² θ in terms of tan θ.

Answer 1

Answer:

sec⁴θ - sec²θ = tan⁴θ + tan²θ

Step-by-step explanation:

sec⁴ θ -sec² θ = (sec²θ)² -sec²θ

                        =  (1 + tan²θ)² -( 1 + tan²θ)        ∵ tan²θ + 1 = sec² θ

                        = 1 + tan⁴θ + 2tan²θ - 1 - tan²θ

                        = tan⁴θ + tan²θ

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