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JEE Main & Advanced Mathematics Trigonometric Equations Question Bank Solution of trigonometrical equations

  • question_answer
    If \[0\le x\le \pi \]and \[{{81}^{{{\sin }^{2}}x}}+{{81}^{{{\cos }^{2}}x}}=30\], then x = [Karnataka CET 2004]

    A) \[\pi /6\]

    B) \[\pi /2\]

    C) \[\pi /4\]

    D) \[3\pi /4\]

    Correct Answer: A

    Solution :

    We have, \[{{81}^{{{\sin }^{2}}x}}+{{81}^{{{\cos }^{2}}x}}=30\] Now check by options, put \[x=\frac{\pi }{6}\] then \[{{(81)}^{{{\sin }^{2}}\pi /6}}+{{(81)}^{{{\cos }^{2}}\pi /6}}=30\] Þ  \[{{(81)}^{1/4}}+{{(81)}^{3/4}}=30\] Þ 30 = 30 Hence A is the correct answer.


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