What is the general solution for solvefor u,x=tanh(u) ?

The general solution for solvefor u,x=tanh(u) is u= 1/2 ln((x+1)/(1-x)),u=ln(-sqrt((x+1)/(1-x)))

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solvefor u,x=tanh(u)

solve for

u, x = tanh (u)

u = \frac{1}{2} ln (\frac{x + 1}{1 - x}), u = ln (- \frac{x + 1}{1 - x})

Solution steps

x = tanh (u)

Switch sides

tanh (u) = x

Rewrite using trig identities

\frac{e ^{u} - e ^{- u}}{e ^{u} + e ^{- u}} = x

\frac{e ^{u} - e ^{- u}}{e ^{u} + e ^{- u}} = x : u = \frac{1}{2} ln (\frac{x + 1}{1 - x}) {- 1 < x < 1}, u = ln (- \frac{x + 1}{1 - x}) {No Solution}

u = \frac{1}{2} ln (\frac{x + 1}{1 - x}), u = ln (- \frac{x + 1}{1 - x})

3 + 2 cos (x) = 0

2 cos^{2} (θ) - 7 cos (θ) = - 3

tan^{2} (x) = 3 - 2 tan (x)

tan (3 x) + tan (5 x) = 0

sin (x) = \frac{1}{2} 3

What is the general solution for solvefor u,x=tanh(u) ?
The general solution for solvefor u,x=tanh(u) is u= 1/2 ln((x+1)/(1-x)),u=ln(-sqrt((x+1)/(1-x)))