Question

The general solution of the equation $\tan 5\theta =\cot 3\theta$ is given by

• A.
  $\theta =\frac{n\pi }{8}-\frac{\pi }{16},n\in Z.$
• B.
  $\theta =\frac{n\pi }{8}+\frac{\pi }{16},n\in Z.$
• C.
  $\theta =\frac{n\pi }{8}+\frac{\pi }{8},n\in Z.$
• D.
  $\theta =\frac{n\pi }{8}-\frac{\pi }{8},n\in Z.$

Answer 1

The correct option is B

$\theta =\frac{n\pi }{8}+\frac{\pi }{16},n\in Z.$
Here, we can write the equation as:
$\tan 5\theta =cot3\theta \Rightarrow \tan 5\theta =\tan \left(\frac{\pi }{2}-3\theta \right)\Rightarrow 5\theta =n\pi +\frac{\pi }{2}-3\theta ,n\in Z\Rightarrow 8\theta =n\pi +\frac{\pi }{2},n\in Z\Rightarrow \theta =\frac{n\pi }{8}+\frac{\pi }{16},n\in Z$
Thus, Option b is correct.