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TS EAMCET · Maths · Trigonometric Ratios & Identities

If \(\tan x+\tan \left(x+\frac{\pi}{3}\right)+\tan \left(x+\frac{2 \pi}{3}\right)=3\) then \(\tan 3 x\) is equal to

  1. A \(3\)
  2. B \(2\)
  3. C \(1\)
  4. D \(0\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(1\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { LHS }=\tan x+\tan \left(x+\frac{\pi}{3}\right)+\tan \left(x+\frac{2 \pi}{3}\right) \\ & =\tan x+\frac{\tan x+\sqrt{3}}{1-\sqrt{3} \tan x}+\frac{\tan x-\sqrt{3}}{1+\sqrt{3} \tan x} \\ & =\tan x+\frac{\left[\begin{array}{c}(\tan x+\sqrt{3})(1+\sqrt{3}…