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Show that the equation e^(sinx)-e^(-sinx...

Show that the equation `e^(sinx)-e^(-sinx)-4=0` has no real solution.

Text Solution

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`e^(sinx)-e^(-sinx)-4=0`
`e^(sinx)-1/(e^(sinx))-4=0`
`((e^(sinx))^2-1)/(e^(sinx))=4`
`(e^(sinx))^2-4e^(sinx)-1=0`
`e^(sinx)=(4pmsqrt20)/2=(4pm2sqrt5)/2`
`e^(sinx)=2pmsqrt5=2pm2.73`
`=-0.236`
`0lte^(sinx)lte`.
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Knowledge Check

  • e^(sinx)-e^(-sinx)=4 for

    A
    all real values of x
    B
    some `x in [0, pi//2]`
    C
    some `x in (-pi//2, pi//2)`
    D
    no real value of x

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