2 cosh 2x − sinh 2x = 2
You asked:
Solve the equation \(2 \cdot \cosh\left( 2 x \right) - \sinh\left( 2 x \right) = 2\) for the variable \(x\).
MathBot Answer:
The real solutions are: \[\begin{aligned}x &=0\\x &=\frac{\log{\left(3 \right)}}{2}\end{aligned}\]
The complex solutions are: \[\begin{aligned}x &= \left\{\pi i n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{3.1415927 n i\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\frac{\log{\left(3 \right)}}{2} + \pi i n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{3.1415927 n i + 0.54930614\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).