Question

Solve $2\tan \theta -\cot \theta =-1$

• A. $\theta =n\pi +(-\frac{\pi }{2})$
• B. $\theta =m\pi -\alpha$
• C. $\theta =n\pi +(-\frac{\pi }{4})$
• D. $\theta =m\pi +\alpha$

Answer 1

Answer: (C), (D)

The correct options are
C $\theta =n\pi +(-\frac{\pi }{4})$
D $\theta =m\pi +\alpha$

$2\tan \theta -\cot \theta =-1$
or $2\tan \theta -\frac{1}{\tan \theta }=-1$
or $2{\tan }^2\theta +\tan \theta -1=0$
or $(\tan \theta +1)\left(2\tan \theta 1\right)=0$
or $\tan \theta =-1$ or $\tan \theta =\frac{1}{2}$
or
$\tan \theta =\tan (-\frac{\pi }{4})$
or $\tan \theta =\tan \left({\tan }^{-1}\frac{1}{2}\right)$
$\Rightarrow$ $\theta =n\pi +(-\frac{\pi }{4})$ or $\theta =m\pi +\alpha$, where $m,nϵZ$ and $\tan \alpha =\frac{1}{2}$