What is the general solution for solvefor u,x=2tanh(u) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

solvefor u,x=2tanh(u)

solve for

u, x = 2 tanh (u)

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

Solution steps

x = 2 tanh (u)

Switch sides

2 tanh (u) = x

Rewrite using trig identities

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

2 \cdot \frac{e ^{u} - e ^{- u}}{e ^{u} + e ^{- u}} = x : u = \frac{1}{2} ln (\frac{x + 2}{2 - x}), u = ln (- \frac{x + 2}{2 - x})

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

4 cos^{2} (x) + cos (2 x) - 7 cos (x) = - 2

4 cos (x) = 2 + 2 cos (x)

4 cos (θ) = 43 sin (θ)

- 4 sin (θ) = 4 (sin (θ) - 1)

4 + 2 cos (θ) = 0

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