What is the general solution for coth^2(x)+csch^2(x)=2 ?

The general solution for coth^2(x)+csch^2(x)=2 is x= 1/2 ln(5-2sqrt(6)),x= 1/2 ln(5+2sqrt(6))

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coth^2(x)+csch^2(x)=2

coth^{2} (x) + csch^{2} (x) = 2

x = \frac{1}{2} ln (5 - 26), x = \frac{1}{2} ln (5 + 26)

Solution steps

coth^{2} (x) + csch^{2} (x) = 2

Rewrite using trig identities

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

(\frac{e ^{x} + e ^{- x}}{e ^{x} - e ^{- x}})^{2} + (\frac{2}{e ^{x} - e ^{- x}})^{2} = 2 : x = \frac{1}{2} ln (5 - 26), x = \frac{1}{2} ln (5 + 26)

x = \frac{1}{2} ln (5 - 26), x = \frac{1}{2} ln (5 + 26)

tan (x) = \frac{3}{9}

2 cos (x) = 3 cot (x)

sin^{2} (x) + 2 sin (x) - 1 = 0

1 = cos^{3} (x)

sin (θ) = \frac{150 N}{212.6 N} (0.9063)

What is the general solution for coth^2(x)+csch^2(x)=2 ?
The general solution for coth^2(x)+csch^2(x)=2 is x= 1/2 ln(5-2sqrt(6)),x= 1/2 ln(5+2sqrt(6))