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    Question

    If '╬╕' is an angle less than 120┬░, what is

    the value of '╬╕' if it satisfies the equation 3cos2╬╕ = 2 + sin2╬╕.
    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, 3cos2╬╕ = 2 + sin2╬╕

    Or, 3cos2╬╕ - sin2┬а╬╕ = 2

    Or, 3cos2╬╕ - (1 - cos2┬а╬╕) = 2

    Or, 4cos2╬╕ = 3

    Or, cos2╬╕ = (3/4)

    Or, cos╬╕ = тИЪ3/2 (Since, in options maximum value of '╬╕' is 90o┬аtherefore, we will take the positive root only)

    Or, cos╬╕ = cos30o

    So, ╬╕ = 30o

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