[JEE Advanced 2005] If $\cos(\alpha-\beta)=1$ and $\cos(\alpha+\beta)=\frac1e$ with $\alpha,\beta\in[-\pi,\pi]$, the number of pairs $(\alpha,\beta)$ satisfying both is
If $\cos(\alpha-\beta)=1$ and $\cos(\alpha+\beta)=\frac1e$ with $\alpha,\beta\in[-\pi,\pi]$, the number of pairs $(\alpha,\beta)$ satisfying both is
(a) $0$
(b) $1$
(c) $2$
(d) $4$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 1mo ago
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Correct answer: (d) $4$
$\cos(\alpha-\beta)=1\Rightarrow\alpha=\beta$ (within range, also $\alpha-\beta=\pm2\pi$ edge). Then $\cos2\alpha=\frac1e$ gives $4$ values of $\alpha$ in $[-\pi,\pi]$, hence $4$ pairs.
JEE Advanced 2005 · Trigonometry — verified solution by the Vidaara Team.
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