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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.

A

infinite number of real roots

B

no real roots

C

exactly one real root

D

exactly four real roots

Text Solution

Verified by Experts

The correct Answer is:
B
Let ` e^(sin x) = t`
` rArr t^(2) - 4t - 1= 0`
` rArr t = (4 pm sqrt(16+4))/2`
` rArr t=e^(sin x) = 2 pm sqrt5`
` rArr e^(sin x) = 2 - sqrt5, e^(sin x ) = 2 + sqrt 5 `
` e ^(sin x ) = 2 - sqrt 5 lt 0 ` ,
` rArr sin x = "In " (2+sqrt5) gt 1`
So it is rejected, hence there is no solution.
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