- Home
- Standard 11
- Mathematics
Trigonometrical Equations
medium
यदि $\cos \theta + \cos 2\theta + \cos 3\theta = 0$, तब $\theta $ का व्यापक मान होगा
A
$\theta = 2m\pi \pm \frac{{2\pi }}{3}$
B
$\theta = 2m\pi \pm \frac{\pi }{4}$
C
$\theta = m\pi \pm {( - 1)^m}\frac{{2\pi }}{3}$
D
$(a)$ और $(b)$ दोनों
Solution
$\cos \theta + \cos 2\theta + \cos 3\theta = 0$
$(\cos \theta + \cos 3\theta ) + \cos 2\theta = 0$
$2\cos 2\theta \cos \theta + \cos 2\theta = 0$
$\cos 2\theta (2\cos \theta + 1) = 0$
$\cos 2\theta = 0 = \cos \frac{\pi }{2}$
$\theta = \frac{\pi }{4}$
$\Rightarrow$ $\theta = 2m\pi \pm \frac{\pi }{4}$
या $\cos \theta = \frac{{ – 1}}{2} = \cos \frac{{2\pi }}{3}$
$\theta = 2m\pi \pm \frac{{2\pi }}{3}$.
Standard 11
Mathematics
