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Find the number of solution of the equat...

Find the number of solution of the equation `e^(sinx)-e^(-sinx)-4=0`

Text Solution

Verified by Experts

Put `e^(sin x)=t`
`rArr t^(2)-4t-1=0`
`rArr t=e^(sin x)=2 pm sqrt(5)`
Now `sin x in [-1, 1]`. Thus,
`e^(sin x) in [e^(-1), e^(1)]` and `2 pm sqrt(5) notin [e^(-1), e^(1)]`
Hence, there does not exist any solution.
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