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

  • question_answer
    The number of solution of the equation \[2\cos ({{e}^{x}})={{5}^{x}}+{{5}^{-x}}\], are          [UPSEAT 2004; IIT 1992]

    A) No solution

    B) One solution

    C) Two solutions

    D) Infinitely many solutions

    Correct Answer: A

    Solution :

    We know \[\frac{{{5}^{x}}+{{5}^{-x}}}{2}\ge 1\],  (using A.M. \[\ge \] G.M.) But since \[\text{cos}\,({{e}^{x}})\le 1\] So, there does not exist any solution.


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