The general solution of $\frac{1-\cos 2 x}{1+\cos 2 x}=3$ is

The general solution of $\frac{1-\cos 2 x}{1+\cos 2 x}=3$ is
  1. $x=2 n \pi \pm \frac{\pi}{3}, n \in Z$
  2. $\quad x=n \pi \pm \frac{\pi}{6} \quad, n \in Z$
  3. $x=2 \mathrm{n} \pi \pm \frac{\pi}{6}, \mathrm{n} \in \mathrm{Z}$
  4. $x=\mathrm{n} \pi \pm \frac{\pi}{3}, \mathrm{n} \in \mathrm{z}$

Solution

$\frac{1-\cos 2 x}{1+\cos 2 x}=3 \Rightarrow \frac{2 \sin ^{2} x}{2 \cos ^{2} x}=3$ $\therefore \tan ^{2} x=3 \Rightarrow \tan ^{2} x=\tan ^{2} \frac{\pi}{3} \Rightarrow x=n \pi \pm \frac{\pi}{3}$

Asked in: MHT CET 2020 (20 Oct Shift 1)

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