[JEE Main 2004] if pi alpha beta 3 pi sin alpha sin beta 21 65 and cos
If $\pi<\alpha-\beta<3\pi$, $\sin\alpha+\sin\beta=-\frac{21}{65}$ and $\cos\alpha+\cos\beta=-\frac{27}{65}$, then $\cos\frac{\alpha-\beta}2$ is
(a) $-\frac6{65}$
(b) $\frac3{\sqrt{130}}$
(c) $\frac6{65}$
(d) $-\frac3{\sqrt{130}}$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 2d ago
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Correct answer: (d) $-\frac3{\sqrt{130}}$
$(\sin\alpha+\sin\beta)^2+(\cos\alpha+\cos\beta)^2=4\cos^2\frac{\alpha-\beta}2=\frac{1170}{4225}\Rightarrow\cos^2\frac{\alpha-\beta}2=\frac9{130}$. With $\frac{\alpha-\beta}2\in(\frac\pi2,\frac{3\pi}2)$, $\cos<0$: $-\frac3{\sqrt{130}}$.
JEE Main 2004 · Trigonometry — verified solution by the Vidaara Team.
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