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Trigonometrical Equations
easy
અંતરાલ $[0,\,\,2\pi ]$ માં સમીકરણ $(5 + 4\cos \theta )(2\cos \theta + 1) = 0$ નો ઉકેલગણ મેળવો.
A
$\left\{ {\frac{\pi }{3},\,\frac{{2\pi }}{3}} \right\}$
B
$\left\{ {\frac{\pi }{3},\,\pi } \right\}$
C
$\left\{ {\frac{{2\pi }}{3},\frac{{4\pi }}{3}} \right\}$
D
$\left\{ {\frac{{2\pi }}{3},\frac{{5\pi }}{3}} \right\}$
Solution
(c) $(5 + 4\cos \theta )(2\cos \theta + 1) = 0$
$\cos \theta = – 5/4$, which is not possible.
$\therefore 2\cos \theta + 1 = 0$ or $\cos \theta = – 1/2$
==> $\theta = \frac{{2\pi }}{3},\,\,\frac{{4\pi }}{3}.$
Solution set is $\left\{ {\frac{{2\pi }}{3},\,\,\frac{{4\pi }}{3}} \right\} \in [0,\,\,2\pi ]$.
Standard 11
Mathematics
