What is the general solution for 12cosh(2x)+7sinh(x)-24=0 ?

The general solution for 12cosh(2x)+7sinh(x)-24=0 is x=ln(1.73025…),x=ln(0.45623…)

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12cosh(2x)+7sinh(x)-24=0

12 cosh (2 x) + 7 sinh (x) - 24 = 0

x = ln (1.73025 \dots), x = ln (0.45623 \dots)

Solution steps

12 cosh (2 x) + 7 sinh (x) - 24 = 0

Rewrite using trig identities

12 \cdot \frac{e ^{2 x} + e ^{- 2 x}}{2} + 7 \cdot \frac{e ^{x} - e ^{- x}}{2} - 24 = 0

12 \cdot \frac{e ^{2 x} + e ^{- 2 x}}{2} + 7 \cdot \frac{e ^{x} - e ^{- x}}{2} - 24 = 0 : x = ln (1.73025 \dots), x = ln (0.45623 \dots)

x = ln (1.73025 \dots), x = ln (0.45623 \dots)

sec^{2} (θ) - 1 = 0

2 sin (θ) cos (θ) = - sin (θ)

6 cos (c) - 4 = cos (c) - 9

sec (θ) = \frac{7}{6}

2 cos^{2} (x) + 7 sin (x) - 5 = 0

What is the general solution for 12cosh(2x)+7sinh(x)-24=0 ?
The general solution for 12cosh(2x)+7sinh(x)-24=0 is x=ln(1.73025…),x=ln(0.45623…)