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

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

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cosh(x-1)=2

cosh (x - 1) = 2

x = ln (e (2 + 3)), x = ln (e (2 - 3))

Solution steps

cosh (x - 1) = 2

Rewrite using trig identities

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

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

x = ln (e (2 + 3)), x = ln (e (2 - 3))

tan (x) = \frac{7}{25}

tan (x) = - 1, 0 < x < 2 π

sec^{2} (x) - 2 = tan^{2} (x), 0 \leq x \leq 2 π

sin (\frac{1}{2} x) = - \frac{1}{2}

4 cos (x) - 3 cos (x) - 1 = 0

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