2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Trigonometric Identities

JEE Main & Advanced Mathematics Trigonometric Identities Question Bank Self Evaluation Test - Trigonometric Function

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

    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 \[{{(81)}^{{{\sin }^{2}}\pi /6}}+{{(81)}^{{{\cos }^{2}}\pi /6}}=30\] \[\Rightarrow \,\,{{(81)}^{1/4}}+{{(81)}^{3/4}}=30\Rightarrow 30=30\]


You need to login to perform this action.
You will be redirected in 3 sec spinner