Question

If tan⁻¹ 3 + tan⁻¹ x = tan⁻¹ 8, then x =

Options

• 5

• 1/5

• 5/14

• 14/5

Answer 1

(b) `1/5`

We know that 
\[\tan^{- 1} x + \tan^{- 1} y = \tan^{- 1} \frac{x + y}{1 - xy}\]
Now,
\[\tan^{- 1} 3 + \tan^{- 1} x = \tan^{- 1} 8\]
\[ \Rightarrow \tan^{- 1} \left( \frac{3 + x}{1 - 3x} \right) = \tan^{- 1} 8\]
\[ \Rightarrow \frac{3 + x}{1 - 3x} = 8\]
\[ \Rightarrow 3 + x = 8 - 24x\]
\[ \Rightarrow 3 - 8 = - 24x - x\]
\[ \Rightarrow - 5 = - 25x\]
\[ \Rightarrow x = \frac{5}{25} = \frac{1}{5}\]
\[\]