What is the general solution for 3tanh^2(x)=5sech(x)+1 ?

The general solution for 3tanh^2(x)=5sech(x)+1 is x=ln(0.17157…),x=ln(5.82842…)

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3tanh^2(x)=5sech(x)+1

3 tanh^{2} (x) = 5 sech (x) + 1

x = ln (0.17157 \dots), x = ln (5.82842 \dots)

Solution steps

3 tanh^{2} (x) = 5 sech (x) + 1

Rewrite using trig identities

3 (\frac{e ^{x} - e ^{- x}}{e ^{x} + e ^{- x}})^{2} = 5 \cdot \frac{2}{e ^{x} + e ^{- x}} + 1

3 (\frac{e ^{x} - e ^{- x}}{e ^{x} + e ^{- x}})^{2} = 5 \cdot \frac{2}{e ^{x} + e ^{- x}} + 1 : x = ln (0.17157 \dots), x = ln (5.82842 \dots)

x = ln (0.17157 \dots), x = ln (5.82842 \dots)

tan (θ) = \frac{5}{7}

(cot (x) - 1) (3 tan (x) + 1) = 0

cos (2 θ - \frac{π}{2}) = \frac{2}{2}

tan^{3} (x) + tan^{2} (x) - 3 tan (x) = 3

cos (x) = \frac{7}{9}

What is the general solution for 3tanh^2(x)=5sech(x)+1 ?
The general solution for 3tanh^2(x)=5sech(x)+1 is x=ln(0.17157…),x=ln(5.82842…)