The general solution of $\tan 3 x=1$ is

The general solution of $\tan 3 x=1$ is
  1. $x=n \pi, n \in Z$
  2. $x=n\left(\frac{\pi}{3}\right)+\frac{\pi}{12}, n \in Z$
  3. $x=n \pi+\frac{\pi}{4}, n \in Z$
  4. $x=n \pi \pm \frac{\pi}{4}, n \in Z$

Solution

We know that $\tan \theta=\tan \alpha$ implies $\theta=n \pi+\alpha$, where $n \in Z$ Given $\tan 3 x=1$ $\therefore \tan 3 x=\tan \frac{\pi}{4} \Rightarrow 3 x=n \pi+\frac{\pi}{4}$ $\therefore \quad \mathrm{x}=\frac{\mathrm{n} \pi}{3}+\frac{\pi}{12}, \quad \mathrm{n} \in Z$

Asked in: MHT CET 2020 (14 Oct Shift 1)

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