What is the general solution for cosh(2x)+sinh^2(x)-13sinh(x)=-3 ?

The general solution for cosh(2x)+sinh^2(x)-13sinh(x)=-3 is x=ln(1.38742…),x=ln(8.12310…)

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cosh(2x)+sinh^2(x)-13sinh(x)=-3

cosh (2 x) + sinh^{2} (x) - 13 sinh (x) = - 3

x = ln (1.38742 \dots), x = ln (8.12310 \dots)

Solution steps

cosh (2 x) + sinh^{2} (x) - 13 sinh (x) = - 3

Rewrite using trig identities

\frac{e ^{2 x} + e ^{- 2 x}}{2} + (\frac{e ^{x} - e ^{- x}}{2})^{2} - 13 \cdot \frac{e ^{x} - e ^{- x}}{2} = - 3

\frac{e ^{2 x} + e ^{- 2 x}}{2} + (\frac{e ^{x} - e ^{- x}}{2})^{2} - 13 \cdot \frac{e ^{x} - e ^{- x}}{2} = - 3 : x = ln (1.38742 \dots), x = ln (8.12310 \dots)

x = ln (1.38742 \dots), x = ln (8.12310 \dots)

sin (3 x - \frac{π}{4}) = 1

\frac{1 - tan ^{2} ( A )}{1 + tan ^{2} ( A )} = 1

sin (2 x) - 0.8 = 0

tan (a) = \frac{15}{7}, sin (a)

2 cos^{2} (θ) + sin (θ) = 2

What is the general solution for cosh(2x)+sinh^2(x)-13sinh(x)=-3 ?
The general solution for cosh(2x)+sinh^2(x)-13sinh(x)=-3 is x=ln(1.38742…),x=ln(8.12310…)