Q. The most general value of $\theta$ satisfying the equations $\sin{\theta = \sin\alpha}$ and $\cos{\theta = \cos\alpha}$ is
A) $2n\pi + \alpha$
B) $2n\pi - \alpha$
C) $n\pi + \alpha$
D) $n\pi - \alpha$
Explanation
(c)
Since, $\sin{\theta = \sin\alpha}$ …(i)
And $\cos{\theta = \cos\alpha}$ …(ii)
[divided Eq. (i) by Eq. (ii)]
$\therefore\ \ \tan{\theta = \tan\alpha}$
$\Rightarrow \ \ \theta = n\pi + \alpha$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.