What is the general solution for 4tanh(x)-1/(cosh(x))=1 ?

The general solution for 4tanh(x)-1/(cosh(x))=1 is x=ln(5/3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4tanh(x)-1/(cosh(x))=1

4 tanh (x) - \frac{1}{cosh ( x )} = 1

x = ln (\frac{5}{3})

Solution steps

4 tanh (x) - \frac{1}{cosh ( x )} = 1

Rewrite using trig identities

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

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

x = ln (\frac{5}{3})

2 sin (θ) cos (θ) = sin (θ)

53 cot (x) + 5 = 0

cos (θ) = - \frac{11}{6}

sin^{2} (x) - csc^{2} (x) = tan^{2} (x) - cot^{2} (x)

sin (x) = \frac{53}{54}

What is the general solution for 4tanh(x)-1/(cosh(x))=1 ?
The general solution for 4tanh(x)-1/(cosh(x))=1 is x=ln(5/3)