What is the general solution for solvefor u,x=5sinh(u) ?

The general solution for solvefor u,x=5sinh(u) is u=ln((x+sqrt(x^2+25))/5),u=ln((x-sqrt(x^2+25))/5)

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solvefor u,x=5sinh(u)

solve for

u, x = 5 sinh (u)

u = ln (\frac{x + x ^{2} + 25}{5}), u = ln (\frac{x - x ^{2} + 25}{5})

Solution steps

x = 5 sinh (u)

Switch sides

5 sinh (u) = x

Rewrite using trig identities

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

5 \cdot \frac{e ^{u} - e ^{- u}}{2} = x : u = ln (\frac{x + x ^{2} + 25}{5}), u = ln (\frac{x - x ^{2} + 25}{5})

u = ln (\frac{x + x ^{2} + 25}{5}), u = ln (\frac{x - x ^{2} + 25}{5})

sin (\frac{π}{2} x) + 1 = 0

3 tan^{2} (x) - tan (x) = 0

sin (2 x) = - \frac{1}{2}, 0 \leq x \leq 2 π

x, 2 sin (x) - 3 = 0

cot (θ + 10 0^{\circ}) = 0

What is the general solution for solvefor u,x=5sinh(u) ?
The general solution for solvefor u,x=5sinh(u) is u=ln((x+sqrt(x^2+25))/5),u=ln((x-sqrt(x^2+25))/5)