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    Question

    Given that 'θ' is an angle less than 120°, what is the

    value of 'θ' if it satisfies the equation 7cos² θ = 1 + 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, 7cos²θ = 1 + sin²θ Or 7cos²θ - sin² θ = 1 Or 7cos²θ - (1 - cos²θ) = 1 Or 8cos²θ = 2 Or cos²θ = (2/8) =1/4 Or cosθ = 1/2 (Since, in options maximum value of 'θ' is 90°therefore, we will take the positive root only) Or cosθ = cos60° θ=60°

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