What is the general solution for 1+7sinh(x)=4cosh^2(x) ?

The general solution for 1+7sinh(x)=4cosh^2(x) is x=ln(2),x=ln(1+sqrt(2))

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1+7sinh(x)=4cosh^2(x)

1 + 7 sinh (x) = 4 cosh^{2} (x)

x = ln (2), x = ln (1 + 2)

Solution steps

1 + 7 sinh (x) = 4 cosh^{2} (x)

Rewrite using trig identities

1 + 7 \cdot \frac{e ^{x} - e ^{- x}}{2} = 4 (\frac{e ^{x} + e ^{- x}}{2})^{2}

1 + 7 \cdot \frac{e ^{x} - e ^{- x}}{2} = 4 (\frac{e ^{x} + e ^{- x}}{2})^{2} : x = ln (2), x = ln (1 + 2)

x = ln (2), x = ln (1 + 2)

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

cos^{2} (x) + 6 cos (x) + 5 = 0

sin (t) = - 0.9397

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

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

What is the general solution for 1+7sinh(x)=4cosh^2(x) ?
The general solution for 1+7sinh(x)=4cosh^2(x) is x=ln(2),x=ln(1+sqrt(2))