TS EAMCET · Maths · Inverse Trigonometric Functions
The number of real solutions of \(\operatorname{Tan}^{-1} x+\operatorname{Tan}^{-1} 2 x=\frac{\pi}{4}\) is
- A 2
- B 1
- C 0
- D infinitely many
Answer & Solution
Correct Answer
(B) 1
Step-by-step Solution
Detailed explanation
\(\operatorname{Tan}^{-1}\left(\frac{x+2x}{1-x(2x)}\right) = \frac{\pi}{4}\) \(\frac{3x}{1-2x^2} = \operatorname{Tan}\left(\frac{\pi}{4}\right)\) \(\frac{3x}{1-2x^2} = 1\) \(3x = 1-2x^2\) \(2x^2 + 3x - 1 = 0\) \(x = \frac{-3 \pm \sqrt{3^2 - 4(2)(-1)}}{2(2)}\)…
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