Question

    If θ is a positive acute angle and cos²

    θ + cos⁴θ = 1, then the value of tan²θ + tan⁴θ is?
    A 1 Correct Answer Incorrect Answer
    C √2 Correct Answer Incorrect Answer
    D √3 Correct Answer Incorrect Answer

    Solution

    cos² θ + cos ⁴ θ = 1 cos ⁴ θ = 1 - cos² θ cos ⁴ θ = sin² θ cos² θ = sin² θ/ cos² θ tan² θ = cos² θ tan² θ = cos ⁴ θ tan² θ + tan ⁴ θ = cos² θ + cos ⁴ θ = 1

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