[JEE Main 2012] the equation e sin x e sin x 4 0 has
The equation $e^{\sin x}-e^{-\sin x}-4=0$ has
(a) infinitely many real roots
(b) no real roots
(c) exactly one real root
(d) exactly four real roots
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
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Correct answer: (b) no real roots
Put $t=e^{\sin x}\in[e^{-1},e]$: $t-\frac1t=4\Rightarrow t=2+\sqrt5\approx4.24>e$, impossible. No real roots.
JEE Main 2012 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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