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Trigonometrical Equations
easy
સમીકરણ $2{\sin ^2}\theta + \sqrt 3 \cos \theta + 1 = 0$ નું સમાધાન કરે તેવા $\theta $ ની ન્યૂનતમ કિમત મેળવો.
A
$\frac{{5\pi }}{6}$
B
$\frac{{2\pi }}{3}$
C
$\frac{\pi }{3}$
D
$\frac{\pi }{6}$
Solution
$2 – 2{\cos ^2}\theta + \sqrt 3 \cos \theta + 1 = 0$
$ \Rightarrow $ $2{\cos ^2}\theta – \sqrt 3 \cos \theta – 3 = 0$
$ \Rightarrow $ $\cos \theta = \frac{{\sqrt 3 \pm \sqrt {3 + 24} }}{4} = \frac{{\sqrt 3 (1 \pm 3)}}{4} = \sqrt 3 \left( { – \frac{1}{2}} \right)$
$ \Rightarrow $ $\theta = \frac{{5\pi }}{6}$.
Standard 11
Mathematics
