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    Question

    If tan 4θ = cot 14θ, then find the value of cos 9θ.

    A 1/√2 Correct Answer Incorrect Answer
    B 1 Correct Answer Incorrect Answer
    C √3/2 Correct Answer Incorrect Answer

    Solution

    tan 4θ = cot 14θ

    Or, tan 4θ = cot (90o - 4θ) [because, tan A = cot (90o - A) ]

    Or, 14θ = 90o - 4θ

    Or, 18θ = 90o

    Or, θ = (90/18) o = 5o

    So, cos 9θ = cos 45o = (1/√2)

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