What is the general solution for cosh(4x)=16sinh(x)+1 ?

The general solution for cosh(4x)=16sinh(x)+1 is x=0,x=ln(2.41421…)

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cosh(4x)=16sinh(x)+1

cosh (4 x) = 16 sinh (x) + 1

x = 0, x = ln (2.41421 \dots)

Solution steps

cosh (4 x) = 16 sinh (x) + 1

Rewrite using trig identities

\frac{e ^{4 x} + e ^{- 4 x}}{2} = 16 \cdot \frac{e ^{x} - e ^{- x}}{2} + 1

\frac{e ^{4 x} + e ^{- 4 x}}{2} = 16 \cdot \frac{e ^{x} - e ^{- x}}{2} + 1 : x = 0, x = ln (2.41421 \dots)

x = 0, x = ln (2.41421 \dots)

cos (θ) = (\frac{3}{2})

cos (x + \frac{3 π}{4}) + cos (x - \frac{3 π}{4}) = 1

5 - sin (θ) = cos (2 θ)

8 sin (θ) + 43 = 0

x, sin (x) = \frac{3}{2}

What is the general solution for cosh(4x)=16sinh(x)+1 ?
The general solution for cosh(4x)=16sinh(x)+1 is x=0,x=ln(2.41421…)