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

Explanation

`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`.