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    Question

    If 7sin² ϕ + 3cos² ϕ= 4, then find the value

    of ϕ ?
    A 60° Correct Answer Incorrect Answer
    B 30° Correct Answer Incorrect Answer
    C 45° Correct Answer Incorrect Answer
    D 15° Correct Answer Incorrect Answer

    Solution

    7sin²ϕ + 3cos² ϕ= 4sin² ϕ+ 3sin² ϕ +3cos² ϕ = 4 4sin² ϕ+ 3(sin2 ϕ + cos2ϕ) = 4 4sin²ϕ+ 3 (1) = 4 4sin²ϕ + 4 - 3 = 1 4sin²ϕ = 1 sin²ϕ= 1/4 sin ϕ = 1/2 sin30° = 1/2 Hence, ϕ = 30

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