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)

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