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

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.