JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
Considering only the principal values of inverse trigonometric functions, the number of positive real values of \(x\) satisfying \(\tan ^{-1}(x)+\tan ^{-1}(2 x)=\frac{\pi}{4}\) is :
- A more than \(2\)
- B \(1\)
- C \(2\)
- D \(0\)
Answer & Solution
Correct Answer
(B) \(1\)
Step-by-step Solution
Detailed explanation
\(\tan ^{-1} x+\tan ^{-1} 2 x=\frac{\pi}{4} ; x>0 \) \(\Rightarrow \tan ^{-1} 2 x=\frac{\pi}{4}-\tan ^{-1} x\) Taking tan both sides \(\Rightarrow 2 x=\frac{1-x}{1+x} \) \(\Rightarrow 2 x^2+3 x-1=0\) \(x=\frac{-3 \pm \sqrt{9+8}}{8}=\frac{-3 \pm \sqrt{17}}{8} \)…
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