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TS EAMCET · Maths · Inverse Trigonometric Functions

If \(0 \leq x < \frac{3}{4}\) then the number of values of \(x\) satisfying the equation \(\operatorname{Tan}^{-1}(2 x-1)+\operatorname{Tan}^{-1} 2 x=\operatorname{Tan}^{-1} 4 x-\operatorname{Tan}^{-1}(2 x+1)\) is

  1. A \(0\)
  2. B \(1\)
  3. C \(2\)
  4. D \(3\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(1\)

Step-by-step Solution

Detailed explanation

\( \operatorname{Tan}^{-1}(2 x-1)+\operatorname{Tan}^{-1}(2 x+1)=\operatorname{Tan}^{-1} 4 x-\operatorname{Tan}^{-1} 2 x \) \( \operatorname{Tan}^{-1}\left(\frac{(2x-1)+(2x+1)}{1-(2x-1)(2x+1)}\right)=\operatorname{Tan}^{-1}\left(\frac{4x-2x}{1+(4x)(2x)}\right) \)…