Question

The general solution of $\cot \theta+\tan \theta=2$ is

• A. $\theta=\frac{n \pi}{2}+(-1)^{n} \frac{\pi}{6}$
• B. $\theta=\frac{n \pi}{2}+(-1)^{n} \frac{\pi}{8}$
• C. $\theta=n \pi+(-1)^{n} \frac{\pi}{8}$
• D. $\theta=\frac{n \pi}{2}+(-1)^{n} \frac{\pi}{4}$

Answer 1

Answer: (D)

$1=2 \sin 1=2 \sin \theta \cos 1=2 \sin 1=2 \sin \theta \cos \theta $
$\Rightarrow \sin 2 \theta=\sin \frac{\pi}{2} $
$\Rightarrow 2 \theta=n \pi+(-1)^{n} \frac{\pi}{2}$
$ \Rightarrow \theta=\frac{n \pi}{2}+(-1)^{n} \frac{\pi}{4}$