Search any question & find its solution
Question:
Answered & Verified by Expert
If $\sin 6 \theta+\sin 4 \theta+\sin 2 \theta=0$ then the general value of $\theta$ is
Options:
Solution:
1753 Upvotes
Verified Answer
The correct answer is:
$\frac{\mathrm{n} \pi}{4}, \mathrm{n} \pi \pm \frac{\pi}{3}$
Hints : $2 \sin 4 \theta \cos 2 \theta+\sin 4 \theta=0$
$\sin 4 \theta=0$
$2 \cos 2 \theta=-1$
$4 \theta=n \pi$
$\cos 2 \theta=-\frac{1}{2}=\cos \frac{2 \pi}{3}$
$\theta=\frac{n \pi}{4}$
$2 \theta=2 \mathrm{n} \pi \pm \frac{2 \pi}{3}, \Rightarrow \theta=\mathrm{n} \pi \pm \frac{\pi}{3}$
$\sin 4 \theta=0$
$2 \cos 2 \theta=-1$
$4 \theta=n \pi$
$\cos 2 \theta=-\frac{1}{2}=\cos \frac{2 \pi}{3}$
$\theta=\frac{n \pi}{4}$
$2 \theta=2 \mathrm{n} \pi \pm \frac{2 \pi}{3}, \Rightarrow \theta=\mathrm{n} \pi \pm \frac{\pi}{3}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.