Q63 / 160 · AP EAMCET 2024 (22 May Shift 1) · Mathematics

The general solution of the equation $\tan x+\tan 2 x-\tan$ $3 x=0$ is

  • A
    $\left\{x \left\lvert\, x=n \pi \pm \frac{\pi}{3}\right.\right.$ or $\left.\frac{n \pi}{2}, n \in Z\right\}$
  • Correct answer
    B
    $\left\{x \left\lvert\, x=n \pi \pm \frac{\pi}{3}\right.\right.$ or $\left.n \pi, n \in Z\right\}$
  • C
    $\left\{x \left\lvert\, x=n \pi \pm \frac{\pi}{3}\right.\right.$ or $\frac{n \pi}{2}$ or $\left.n \pi, n \in Z\right\}$
  • D
    $\left\{x \left\lvert\, x=n \pi \pm \frac{\pi}{6}\right.\right.$ or $\left.\frac{n \pi}{2}, n \in Z\right\}$

Solution

$\begin{aligned} & \frac{\tan x+\tan 2 x}{1-\tan x \tan 2 x}=\tan 3 x \\ & \Rightarrow \tan x+\tan 2 x-\tan 3 x=-\tan x \tan 2 x \tan 3 x=0 \\ & \Rightarrow \tan x \tan 2 x \tan 3 x=0 \\ & \Rightarrow x=n \pi \text { or } x=\frac{n \pi}{3} \text { or } x=n \pi \pm \frac{\pi}{3} \text { or } n \pi\end{aligned}$

Hence, the correct answer is option: 'B'.

Relevant Questions