Number of real roots of the equation $e^{s i n x} - e^{- s i n x} - 4 = 0$

None of these

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Solution

The correct option is D 0
Let $e^{s i n x} = t$
$t - \frac{1}{t} - 4 = 0 \Rightarrow t = 2 \pm \sqrt{5} \Rightarrow e^{s i n x} = 2 + \sqrt{5}, 2 - \sqrt{5}$
But $e^{s i n x}$ cannot be negative
$∴ e^{s i n x} = 2 + \sqrt{5}$
$\Rightarrow e^{s i n x} > e$
$\Rightarrow s i n x > 1$ , which is not possible.
So, the given equation has no real solution.

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