Prove:(a) cosh1 x = ln(x + x2 1 ), x 1(b) tanh1 x = 12ln 1 + x1 x, 1 <x< 1

Chapter 6, Problem 60

(choose chapter or problem)

Prove:

(a) $\cosh^{-1}x=\ln\left(x+\sqrt{x^2-1}\right),\quad\ \ \ \ x\ge1$

(b) $\tanh^{-1}x=\frac{1}{2}\ln\left(\frac{1+x}{1-x}\right),\quad\ \ \ \ -1<x<1$

Equation Transcription:

${cosh}^{-1}\ x=ln\left({x+\sqrt{{x}^{2}-1}}\right),\ \ \ \ \ x\geq{}1$

${tanh}^{-1}\ x=\frac{1}{2}ln\left({\frac{1+x}{1-x}}\right),\ \ \ \ \ -1<x<1$

Text Transcription:

cosh^-1 x=ln(x+sqrt x^2-1), x geq 1

tanh^-1 x=1/2 ln(frac 1+x / 1-x), -1<x<1

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