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

The general solution for 3sinh(x)+cosh(x)=-2 is x=ln((-1+sqrt(3))/2)

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3sinh(x)+cosh(x)=-2

3 sinh (x) + cosh (x) = - 2

x = ln (\frac{- 1 + 3}{2})

Solution steps

3 sinh (x) + cosh (x) = - 2

Rewrite using trig identities

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

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

x = ln (\frac{- 1 + 3}{2})

cos (2 + 3 \cdot x) - cos (- 0.5) = 0

2 cos (θ) = 1, 0 \leq θ \leq 2 π

arctan (x + 1) + arctan (x - 1) = arctan (\frac{8}{31})

4 cos (2 θ) + 19 = - 22 cos (θ) + 6

8 cos^{2} (x) + 16 cos (x) + 8 = 0

What is the general solution for 3sinh(x)+cosh(x)=-2 ?
The general solution for 3sinh(x)+cosh(x)=-2 is x=ln((-1+sqrt(3))/2)