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જો $\theta $ અને $\phi $ એ લઘુકોણ છે કે જે સમીકરણ $\sin \theta = \frac{1}{2},$ $\cos \phi = \frac{1}{3}$ નું સમાધાન કરે છે તો $\theta + \phi \in $ . . .
A
$\left( {\frac{\pi }{3},\,\frac{\pi }{2}} \right)$
B
$\left( {\frac{\pi }{2},\frac{{2\pi }}{3}} \right)$
C
$\left( {\frac{{2\pi }}{3},\,\frac{{5\pi }}{6}} \right)$
D
$\left( {\frac{{5\pi }}{6},\pi } \right)$
(IIT-2004)
Solution
(b) $\sin \theta = \frac{1}{2} \Rightarrow \theta = \frac{\pi }{6}$
$\cos \phi = \frac{1}{3} \Rightarrow \frac{\pi }{3} < \phi < \frac{\pi }{2}$. .
Thus, $\frac{\pi }{2} < (\theta + \phi ) < \frac{{2\pi }}{3}$.
Standard 11
Mathematics
