2 cotx+2=-1
You asked:
Solve the equation \(2 \cdot \cot\left( x \right) + 2 = -1\) for the variable \(x\).
MathBot Answer:
The principal value in \(0 < x < \pi\) is \(x \approx 2.5535901\)
The real solutions are: \[\begin{aligned}x &= \left\{\pi - \arctan{\left(\frac{2}{3} \right)} + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 2.55359\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{- \arctan{\left(\frac{2}{3} \right)} + 2 \pi + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 5.6951827\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]