Q. General solution of the equation $\cot{\theta - \tan{\theta = 2}}$ is
A) $n\pi + \frac{\pi}{4}$
B) $\frac{n\pi}{2} + \frac{\pi}{8}$
C) $\frac{n\pi}{2} \pm \frac{\pi}{8}$
D) None of these
Explanation
(b)
We have, $\cot{\theta - \tan{\theta = 2}}$
$\Rightarrow \ \cos^{2}{\theta - \sin^{2}{\theta = 2\sin{\theta\cos\theta}}}$
$\Rightarrow \ \cos{2\theta = \sin{2\theta}}$
$\Rightarrow \ \tan{2\theta = \tan{\frac{\pi}{4}\ \Rightarrow \ 2\theta = n\pi + \frac{\pi}{4}}}$
$\Rightarrow \ \theta = \frac{n\pi}{2} + \frac{\pi}{8}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.