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    Question

    If 'θ' is an angle less than 120°, what is

    the value of 'θ' if it satisfies the equation 3cos2θ = 2 + sin2θ.
    A 60° Correct Answer Incorrect Answer
    B 30° Correct Answer Incorrect Answer
    C 90° Correct Answer Incorrect Answer
    D 45° Correct Answer Incorrect Answer

    Solution

    Given, 3cos2θ = 2 + sin2θ

    Or, 3cos2θ - sin2 θ = 2

    Or, 3cos2θ - (1 - cos2 θ) = 2

    Or, 4cos2θ = 3

    Or, cos2θ = (3/4)

    Or, cosθ = √3/2 (Since, in options maximum value of 'θ' is 90o therefore, we will take the positive root only)

    Or, cosθ = cos30o

    So, θ = 30o

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