If cos(α-β)=1 and cos(α+β)= 1e with α,β∈[-π,π], the number of pairs (α,β) satisfying both is (a) 0 (b) 1 (c) 2 (d) 4

Correct answer: (d) 4 cos(α-β)=1→α=β (within range, also α-β=±2π edge). Then 2α= 1e gives 4 values of α in [-π,π], hence 4 pairs. JEE Advanced 2005 · Trigonometry — verified solution by the Vidaara Team.

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[JEE Advanced 2005] if cos alpha beta 1 and cos alpha beta 1e with alpha beta in

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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 · 2d ago ▲ 0

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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