Q. If $\cos{\theta = - \frac{1}{\sqrt{2\ }}}$ and $\tan{\theta = 1}$, then the general value of $\theta$ is
A) $2n\pi + \frac{\pi}{4}$
B) $2(n + 1)\pi + \frac{\pi}{4}$
C) $n\pi + \frac{\pi}{4}$
D) $n\pi \pm \frac{\pi}{4}$
Explanation
(b)
$\because\cos{\theta = - \ }\frac{1}{\sqrt{2\ }}\ \Rightarrow \ \theta = \frac{3\pi}{4},\frac{5\pi}{4}$
and $\tan{\theta = 1\ \Rightarrow \ \theta = \frac{\pi}{4},\frac{5\pi}{4}}$
$\therefore$ The general value is $2n\pi + \frac{5\pi}{4}\ or\ (2n + 1)\pi + \frac{\pi}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.