Theory of Intelligence
12TH•Mathematics•Graphical Representation Of Functions•Question 7

(i)

Prove the following inverse hyperbolic formulae.

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(i)

tanh⁡−1x=12ln⁡(1+x1−x),  x≠1\tanh^{-1} x = \dfrac{1}{2} \ln\left(\dfrac{1 + x}{1 - x}\right),\; x \neq 1

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(ii)
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