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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NTA Abhyas 2020 · Mathematics · Inverse Trigonometric Functions

If 3 ta n ^ - 1 ( 1 2 + 3 ) - ta n ^ - 1 (1)/(3) = ta n ^ - 1...

If 33 tan−1(12+3)−tan−113=tan−11x,ta{n}^{- 1}\left(\dfrac{1}{2 + \sqrt{3}}\right) - ta{n}^{- 1}\dfrac{1}{3} = ta{n}^{- 1}\dfrac{1}{x}, then the value of xx is equal to

Correct answer

2

Step-by-step solution

The given equation can be written as
3tan−1(2−3)=tan−1(1x)+tan−1(13)3ta{n}^{- 1}\left(2 - \sqrt{3}\right) = ta{n}^{- 1}\left(\dfrac{1}{x}\right) + ta{n}^{- 1}\left(\dfrac{1}{3}\right)
⇒3(15o)=tan−11x+131−1x13⇒1=3+x3x−1⇒x=2⇒ 3\left(1{5}^{o}\right) = ta{n}^{- 1}\dfrac{\dfrac{1}{x} + \dfrac{1}{3}}{1 - \dfrac{1}{x}\dfrac{1}{3}} ⇒ 1 = \dfrac{3 + x}{3x - 1} ⇒ x = 2
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