What is the general solution for 4cosh(x)+3sinh(x)=5 ?

The general solution for 4cosh(x)+3sinh(x)=5 is x=ln((5+3sqrt(2))/7),x=ln((5-3sqrt(2))/7)

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4cosh(x)+3sinh(x)=5

4 cosh (x) + 3 sinh (x) = 5

x = ln (\frac{5 + 3 2}{7}), x = ln (\frac{5 - 3 2}{7})

Solution steps

4 cosh (x) + 3 sinh (x) = 5

Rewrite using trig identities

4 \cdot \frac{e ^{x} + e ^{- x}}{2} + 3 \cdot \frac{e ^{x} - e ^{- x}}{2} = 5

4 \cdot \frac{e ^{x} + e ^{- x}}{2} + 3 \cdot \frac{e ^{x} - e ^{- x}}{2} = 5 : x = ln (\frac{5 + 3 2}{7}), x = ln (\frac{5 - 3 2}{7})

x = ln (\frac{5 + 3 2}{7}), x = ln (\frac{5 - 3 2}{7})

tan (θ) = 0.04

csc (θ) = \frac{9}{11}

5 - 7 sin (x) = 2 cos^{2} (x)

cos^{2} (x) - sin^{2} (x) = cos^{2} (x) + 3 cos (x)

cos (x) = 0.117

What is the general solution for 4cosh(x)+3sinh(x)=5 ?
The general solution for 4cosh(x)+3sinh(x)=5 is x=ln((5+3sqrt(2))/7),x=ln((5-3sqrt(2))/7)