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  • The number of real roots of the equation e^sinx+e^-sinx=4 is

The number of real roots of the equation e^sinx+e^-sinx=4 is

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Solution: Given ,   e^sinx+e^-sinx=4

               Put     e^sinx=t     Rightarrow   t+1/t=4

                Rightarrow   t^2-4t+1=0    Rightarrow    (t-2)^2=3

                Rightarrow     t=2pm sqrt3    ,    e^sinx=2pm sqrt3

                Rightarrow    sinx=log_e(2pm sqrt3)=pm log_e(2pm sqrt3)

               As 2+sqrt3> e    ,   log_e(2+sqrt3)> 1

           Thus ,    sinx< -1 or sinx> 1 , Not possible

Posted by

Deependra Verma

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