- Home
- Standard 11
- Mathematics
Trigonometrical Equations
medium
यदि ${\sin ^2}\theta - 2\cos \theta + \frac{1}{4} = 0,$ तो $\theta $ का व्यापक मान है
A
$n\pi \pm \frac{\pi }{3}$
B
$2n\pi \pm \frac{\pi }{3}$
C
$2n\pi \pm \frac{\pi }{6}$
D
$n\pi \pm \frac{\pi }{6}$
Solution
$1 – {\cos ^2}\theta – 2\cos \theta + \frac{1}{4} = 0$
$ \Rightarrow $ ${\cos ^2}\theta + 2\cos \theta – \frac{5}{4} = 0$
$ \Rightarrow $ $\cos \theta = \frac{{ – 2 \pm \sqrt {4 + 5} }}{2} = – 1 \pm \frac{3}{2}$
$\because$ $|\cos \theta |\, \le 1$,
$\because$ $\cos \theta = – 1 – \frac{3}{2}$ संभव नहीं है।
$ \Rightarrow $ $\cos \theta = – 1 + \frac{3}{2} = \frac{1}{2} = \cos \left( {\frac{\pi }{3}} \right)$
$ \Rightarrow $ $\theta = 2n\pi \pm \frac{\pi }{3}$.
Standard 11
Mathematics
