Question

If $\cos 6\theta + \cos 4\theta + \cos 2\theta + 1 = 0$, then the possible values of $x = \frac{37\pi}{24}$ are.

• A. $2\cos^{2}3\theta + 2\cos 3\theta.\cos\theta = 0$
• B. $\Rightarrow$
• C. $4\cos 3\theta\cos 2\theta\cos\theta = 0$
• D. $\Rightarrow$

Answer 1

Answer: (D)

$\Rightarrow$

Answer 2

$(81)^{\sin^{2}\pi/6} + (81)^{\cos^{2}\pi/6} = 30$

$\Rightarrow$ $\tan\theta = \sqrt{3} = \tan\frac{\pi}{3} \Rightarrow \theta = n\pi + \frac{\pi}{3}$

i.e., $- \pi < \theta < 0$

and $\text{Put}n = - 1$

Hence value of $\theta = - \pi + \frac{\pi}{3} = \frac{- 2\pi}{3}\text{or }\frac{- 4\pi}{6}$ between 0 and $\tan\theta + \frac{1}{\sqrt{3}} = 0$ are

$\theta$

i.e., $0{^\circ}$.