TS EAMCET · Maths · Inverse Trigonometric Functions
If \(\tanh ^{-1} x=a \log \left(\frac{1+x}{1-x}\right),|x| < 1\) then \(a\) is equal to
- A 1
- B 2
- C \(\frac{1}{2}\)
- D \(\frac{1}{4}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(\tanh ^{-1} x=a \log \left(\frac{1+x}{1-x}\right),|x| < 1\) ...(i) But \(\tanh ^{-1} x=\frac{1}{2} \log \left(\frac{1+x}{1-x}\right)\) ...(ii) From Eqs. (i) and (ii), we get \(a=\frac{1}{2}\)
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