If 3 tan^(-1)1/(2+√3)-tan^(-1)1/3=tan^(-1)1/x, then the value of x is equal to

Correct answer: 2. The given equation can be written as 3tan^(-1)2-√3=tan^(-1)1/x+tan^(-1)1/3 ⇒315^o=tan^(-1)(1x+13)/(1-1x13)⇒1=(3+x)/(3x-1)⇒x=2

Q9 / 71 · NTA Abhyas (JEE Main) 2020 · Mathematics · Inverse Trigonometric Functions

If $3$ $t a n^{- 1} (\frac{1}{2 + \sqrt{3}}) - t a n^{- 1} \frac{1}{3} = t a n^{- 1} \frac{1}{x},$ then the value of $x$ is equal to

Correct answer: 2

The given equation can be written as

3 t a n^{- 1} (2 - \sqrt{3}) = t a n^{- 1} (\frac{1}{x}) + t a n^{- 1} (\frac{1}{3})

\Rightarrow 3 (1 5^{o}) = t a n^{- 1} \frac{\frac{1}{x} + \frac{1}{3}}{1 - \frac{1}{x} \frac{1}{3}} \Rightarrow 1 = \frac{3 + x}{3 x - 1} \Rightarrow x = 2

Hence, the correct answer is 2.