If e sin x- e -sin x-4-0- then the number of real values of x isA- 0B- 2C- 3D- 1

The correct option is A 0e^sin x e^ sin x=4 e^sin x=4+e^ sin x nbsp; R.H.S. is always greater than 4. Since, sin x ≤ 1, therefore L.H.S. can take e=2.718 as ...

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Standard XII

Mathematics

Monotonically Increasing Functions

If e sin x- e...

Question

If $e^{sin x} - e^{- sin x} - 4 = 0$ , then the number of real values of $x$ is

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Solution

The correct option is A $0$
$e^{sin x} - e^{- sin x} = 4$
$e^{sin x} = 4 + e^{- sin x}$
R.H.S. is always greater than $4$ .
Since, $sin x \leq 1$ , therefore L.H.S. can take $e = 2.718$ as the maximum value.
Hence, no solution exist.

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If esinx−e−sinx−4=0, then the number of real values of x is

The correct option is A 0esinx−e−sinx=4 esinx=4+e−sinx R.H.S. is always greater than 4. Since, sinx≤1, therefore L.H.S. can take e=2.718 as the maximum value. Hence, no solution exist.

If $e^{sin x} - e^{- sin x} - 4 = 0$ , then the number of real values of $x$ is

The correct option is A $0$
$e^{sin x} - e^{- sin x} = 4$
$e^{sin x} = 4 + e^{- sin x}$
R.H.S. is always greater than $4$ .
Since, $sin x \leq 1$ , therefore L.H.S. can take $e = 2.718$ as the maximum value.
Hence, no solution exist.