Question

If 3 tan$\theta$ = cot$\theta$ then $\theta$ = ___________

• A. 30
• B. 60
• C. 45
• D. 15

Answer 1

The correct option is A 30

Given,

$3\tan \left(\theta \right)=\cot \left(\theta \right)$

$3\tan \left(\theta \right)-\cot \left(\theta \right)=0$

$-\frac{\cos \left(\theta \right)}{\sin \left(\theta \right)}+3\cdot \frac{\sin \left(\theta \right)}{\cos \left(\theta \right)}=0$

$\frac{-{\cos }^2\left(\theta \right)+3{\sin }^2\left(\theta \right)}{\cos \left(\theta \right)\sin \left(\theta \right)}=0$

$-{\cos }^2\left(\theta \right)+3{\sin }^2\left(\theta \right)=0$

$(\sqrt{3}\sin \left(\theta \right)+\cos \left(\theta \right))(\sqrt{3}\sin \left(\theta \right)-\cos \left(\theta \right))=0$

$\sqrt{3}\sin \left(\theta \right)+\cos \left(\theta \right)=0:\theta =\frac{5\pi }{6}+\pi n$

$\sqrt{3}\sin \left(\theta \right)-\cos \left(\theta \right)=0:\theta =\frac{\pi }{6}+\pi n$

$\theta =\frac{5\pi }{6}+\pi n,\theta =\frac{\pi }{6}+\pi n$

$\therefore \theta ={150}^{\circ },{30}^{\circ }$