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Trigonometrical Equations
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यदि $\theta $ और $\phi $ न्यूनकोण को सन्तुष्ट करते हैं व $\sin \theta = \frac{1}{2},$ $\cos \phi = \frac{1}{3},$ तो $\theta $+$\phi $ का मान है
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) $\sin \theta = \frac{1}{2} \Rightarrow \theta = \frac{\pi }{6}$
$\cos \phi = \frac{1}{3} \Rightarrow \frac{\pi }{3} < \phi < \frac{\pi }{2}$. अत: $\frac{\pi }{2} < (\theta + \phi ) < \frac{{2\pi0 }}{3}$.
Standard 11
Mathematics
