If secθ = 4/3, what is the value of tan²θ + tan⁴θ?
112/81
We are given secθ = 4/3.
Using identity: sec²θ = 1 + tan²θ
⇒ (4/3)² = 1 + tan²θ ⇒ 16/9 = 1 + tan²θ ⇒ tan²θ = 16/9 - 1 = 7/9
So, tan²θ = 7/9
⇒ tan⁴θ = (7/9)² = 49/81
⇒ tan²θ + tan⁴θ = 7/9 + 49/81 = 63/81 + 49/81 = 112/81
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