[JEE Advanced 1982] Show that $e^{\sin x}-e^{-\sin x}-4=0$ has no real solution.
Show that $e^{\sin x}-e^{-\sin x}-4=0$ has no real solution.
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 1mo ago
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Answer: Proved (no real solution).
With $t=e^{\sin x}\in[e^{-1},e]$, $t-\frac1t=4\Rightarrow t=2+\sqrt5\approx4.24>e$, which is impossible.
JEE Advanced 1982 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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