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Question: Answered & Verified by Expert
If $\tanh ^{-1} x=a \log \left(\frac{1+x}{1-x}\right),|x| < 1$ then $a$ is equal to
MathematicsInverse Trigonometric FunctionsAP EAMCETAP EAMCET 2010
Options:
  • A 1
  • B 2
  • C $\frac{1}{2}$
  • D $\frac{1}{4}$
Solution:
2099 Upvotes Verified Answer
The correct answer is: $\frac{1}{2}$
$\tanh ^{-1} x=a \log \left(\frac{1+x}{1-x}\right),|x| < 1$ ...(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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