Question

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

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

Answer 1

The correct option is B $\theta =\frac{n\pi }{2}+(-1{)}^n\frac{\pi }{4}$

$\cot \theta +\tan \theta =2\frac{1}{\tan \theta }+\tan \theta =2\sin 2\theta =12\theta =n\pi +(-1{)}^n\frac{\pi }{2}\theta =\frac{n\pi }{2}+(-1{)}^n\frac{\pi }{4}$