[JEE Advanced 2004] [Options garbled in source.] If $\theta,\phi$ are acute with $\sin\theta=\frac12$ and $\cos\phi=\frac13$, then $\theta+\phi$ lies in
[Options garbled in source.] If $\theta,\phi$ are acute with $\sin\theta=\frac12$ and $\cos\phi=\frac13$, then $\theta+\phi$ lies in
(a) $\left(\frac\pi2,\frac{2\pi}3\right)$
(b) $\left(\frac{2\pi}3,\frac{5\pi}6\right)$
(c) $\left(\frac{5\pi}6,\pi\right)$
(d) $\left(\frac\pi3,\frac\pi2\right)$
1 Answer
VAVidaara Admin
✓ Vidaara Team
✓ Accepted
· 1mo ago
▲ 0
Correct answer: (a) $\left(\frac\pi2,\frac{2\pi}3\right)$
$\theta=30^\circ$ and $\phi=\cos^{-1}\frac13\approx70.5^\circ$, so $\theta+\phi\approx100.5^\circ\in\left(\frac\pi2,\frac{2\pi}3\right)$.
JEE Advanced 2004 · Trigonometry — verified solution by the Vidaara Team.
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