Question

Se tanh(x)=0,8, determine cosh(x)

Answer 1

Resposta:

$coshx=\pm\frac{5}{3}$

Explicação passo a passo:

cosh²x - senh²x = 1

$\frac{senh}{cosh^2x} =tghx\\\\\frac{senhx}{coshx} =\frac{8}{10} \\\\\frac{senh}{coshx}=\frac{4}{5}\\\\senhx=\frac{4coshx}{5}\\\\cosh^2x-(\frac{4coshx)}{5} ) ^2=1\\\\cosh^2x-\frac{16cosh^2x}{25}=1 \\\\25cosh^2x-16cosh^2x=25\\\\9cosh^2x=25\\\\cosh^2x=\frac{25}{9} \\\\coshx=\pm\frac{5}{3}$