$$\text{If } 3 \cot \theta = \tan \theta \text{ then the principal value of } \theta \text{ is}$$​​​

Correct option is A

Given:

$$3\cot\theta=\tan\theta$$ 

Solution:

$$3\cot\theta=\tan\theta$$ 

$$3\frac{\cos\theta}{\sin\theta}=\frac{\sin\theta}{\cos\theta}$$ 

$$3\cos^2\theta= sin^2\theta$$        ($$\sin^2\theta= 1- \cos^2\theta$$)

$$3\cos^2\theta= 1-\cos^2\theta$$

$$3\cos^2\theta+\cos^2\theta= 1$$ 

$$4\cos^2\theta= 1$$ 

$$\cos^2\theta= \frac14$$

$$\cos\theta= \frac12$$ 

$$\cos\theta= \cos60^\circ$$ 

$$\theta= 60^\circ$$  =     $$60^\circ= \frac{\pi}{3}$$ 

Because $$\pi$$= 180

Option (a)