JEE Main202431 Jan 2024Evening ShiftMathematicsQuadratic EquationActual

The number of solutions, of the equation e sin x − 2 e − sin x = 2 is

Options

A2
Bmore than 2
C1
D0

Correct answer

D. 0

Step-by-step solution

Let, e sin x = t ⇒ t - 2 t = 2 ⇒ t 2 - 2 t - 2 = 0 ⇒ t 2 - 2 t + 1 = 3 ⇒ t - 1 2 = 3 ⇒ t = 1 ± 3 ⇒ t ≈ 2 . 73 , - 0 . 73 not possible ⇒ t ≈ 2 . 73 ⇒ e sin x ≈ 2 . 73 ⇒ sin x ≈ log e 2 . 73 ⇒ sin x > 1 → Not possible So no solutions will be possible for the given equation.

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