What is the general solution for 2cosh^2(x)-3sinh(x)=1 ?

The general solution for 2cosh^2(x)-3sinh(x)=1 is x=ln(1.61803…),x=ln(2.41421…)

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2cosh^2(x)-3sinh(x)=1

2 cosh^{2} (x) - 3 sinh (x) = 1

x = ln (1.61803 \dots), x = ln (2.41421 \dots)

Solution steps

2 cosh^{2} (x) - 3 sinh (x) = 1

Rewrite using trig identities

2 (\frac{e ^{x} + e ^{- x}}{2})^{2} - 3 \cdot \frac{e ^{x} - e ^{- x}}{2} = 1

2 (\frac{e ^{x} + e ^{- x}}{2})^{2} - 3 \cdot \frac{e ^{x} - e ^{- x}}{2} = 1 : x = ln (1.61803 \dots), x = ln (2.41421 \dots)

x = ln (1.61803 \dots), x = ln (2.41421 \dots)

3 cos^{2} (θ) - sin^{2} (θ) = 2

x, y = \frac{4}{π} arccos (\frac{x}{4})

tan (θ) = \frac{2}{1.5}

tan (x) + 3 = 0, 0 \leq x \leq 2 π

55 = 36 cos (\frac{2 π}{60} t) + 39

What is the general solution for 2cosh^2(x)-3sinh(x)=1 ?
The general solution for 2cosh^2(x)-3sinh(x)=1 is x=ln(1.61803…),x=ln(2.41421…)