AP 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
- A \(3\)
- B \(2\)
- C \(1\)
- D \(0\)
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}…
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