1. Tardigrade
  2. Question
  3. Mathematics
  4. Let k= tan -1(( sin (π/18)+ sin (2 π/18)/ cos (π)18+ cos (2 π)18), then k equals

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Let $k=\tan ^{-1}\left(\frac{\sin \frac{\pi}{18}+\sin \frac{2 \pi}{18}}{\cos \frac{\pi}{18}+\cos \frac{2 \pi}{18}}\right)$, then $k$ equals

Inverse Trigonometric Functions

Solution:

$\theta=\tan ^{-1}\left(\frac{\sin \frac{\pi}{18}+\sin \frac{2 \pi}{18}}{\cos \frac{\pi}{18}+\cos \frac{2 \pi}{18}}\right)=\tan ^{-1}\left(\frac{2 \sin \frac{3 \pi}{36} \cos \frac{\pi}{36}}{2 \cos \frac{3 \pi}{36} \cos \frac{\pi}{36}}\right)=\tan ^{-1}\left(\tan \frac{3 \pi}{36}\right)$
$\theta=\frac{3 \pi}{36}$ radian $=\frac{\pi}{12}$