Question

If $0\le \theta \le 2\pi$, solve the equation :

$4\tan \theta +2=2\tan \theta$

• A. $\theta =\frac{3\pi }{4},\frac{7\pi }{4}$
• B. $\theta =\frac{\pi }{2},\frac{5\pi }{4}$
• C. $\theta =\frac{5\pi }{4},\frac{7\pi }{4}$
• D. None of these

Answer 1

The correct option is A $\theta =\frac{3\pi }{4},\frac{7\pi }{4}$

Given, $4\tan \theta +2=2\tan \theta$

$2\tan \theta +2=0$

$\tan \theta =-1$

$\tan \theta <0$ in quadrants II, IV.

$\therefore \theta =(90+45{)}^o,(270+45{)}^o$

$\therefore \theta ={135}^o,{315}^o$

$\theta =\frac{3\pi }{4},\frac{7\pi }{4}$