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Trigonometrical Equations
easy
समीकरण $(5 + 4\cos \theta )(2\cos \theta + 1) = 0$ का अंतराल $[0,\,\,2\pi ]$ में व्यापक हल होगा
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) $(5 + 4\cos \theta )(2\cos \theta + 1) = 0$
$\cos \theta = – 5/4$, जो कि संभव नहीं है
$\therefore 2\cos \theta + 1 = 0$ या $\cos \theta = – 1/2$
==> $\theta = \frac{{2\pi }}{3},\,\,\frac{{4\pi }}{3}.$
अत: हल समुच्चय $\left\{ {\frac{{2\pi }}{3},\,\,\frac{{4\pi }}{3}} \right\} \in [0,\,\,2\pi ]$.
Standard 11
Mathematics
