Number of real roots of the equation e sin x- e -sin x-4-0A- 1B- 2C- 0D- None of these

The correct option is C 0Let e^sin x = t t 1/t 4 = 0 ⇒ t = 2 ±√(5) ⇒ e^sin x = 2 + √(5) , 2 √(5) But e^sin x cannot be negative ∴ e^sin x = 2 + √(5 ...

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Standard XII

Mathematics

Properties of nth Root of a Complex Number

Number of rea...

Question

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

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None of these

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Solution

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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Number of real roots of the equation esinx−e−sinx−4=0

Let esinx=t t−1t−4=0⇒t=2±√5⇒esinx=2+√5,2−√5 But esinx cannot be negative ∴esinx=2+√5 ⇒esinx>e ⇒sinx>1, which is not possible. So, the given equation has no real solution.

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