AP EAMCET · Maths · Inverse Trigonometric Functions
The real values of \(x\) that satisfy the equation \(\tan ^{-1} x+\tan ^{-1} 2 x=\frac{\pi}{4}\) is
- A \(\frac{-3 \pm \sqrt{17}}{4}\)
- B \(-1 \pm \sqrt{3}\)
- C \(\sqrt{3}-1\)
- D \(\frac{\sqrt{17}-3}{4}\)
Answer & Solution
Correct Answer
(D) \(\frac{\sqrt{17}-3}{4}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } \tan ^{-1} x+\tan ^{-1} 2 x=\frac{\pi}{4} \Rightarrow \tan ^{-1} \frac{x+2 x}{1-2 x^2}=\frac{\pi}{4} \\ & \Rightarrow \frac{x+2 x}{1-2 x^2}=1 \Rightarrow 2 x^2+3 x-1=0 \\ & \Rightarrow x=\frac{-3 \pm \sqrt{17}}{4} \Rightarrow x=\frac{-3+\sqrt{17}}{4}…
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