What is the general solution for 2sinh(2x)-10sinh(x)=0 ?

The general solution for 2sinh(2x)-10sinh(x)=0 is x=0,x=ln((5+sqrt(21))/2),x=ln((5-sqrt(21))/2)

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2sinh(2x)-10sinh(x)=0

2 sinh (2 x) - 10 sinh (x) = 0

x = 0, x = ln (\frac{5 + 21}{2}), x = ln (\frac{5 - 21}{2})

Solution steps

2 sinh (2 x) - 10 sinh (x) = 0

Rewrite using trig identities

2 \cdot \frac{e ^{2 x} - e ^{- 2 x}}{2} - 10 \cdot \frac{e ^{x} - e ^{- x}}{2} = 0

2 \cdot \frac{e ^{2 x} - e ^{- 2 x}}{2} - 10 \cdot \frac{e ^{x} - e ^{- x}}{2} = 0 : x = 0, x = ln (\frac{5 + 21}{2}), x = ln (\frac{5 - 21}{2})

x = 0, x = ln (\frac{5 + 21}{2}), x = ln (\frac{5 - 21}{2})

cot (x - \frac{π}{2}) + 1 = 0

- sin (t) + cos (t) = 0

4 cos (x) = 3 sec (x)

2 sin (x) cos (x) = 2 sin (x)

sin^{2} (θ) = 3 - 2 cos^{2} (θ)

What is the general solution for 2sinh(2x)-10sinh(x)=0 ?
The general solution for 2sinh(2x)-10sinh(x)=0 is x=0,x=ln((5+sqrt(21))/2),x=ln((5-sqrt(21))/2)