cosec(x+30)=2
You asked:
Solve the equation \(\csc\left( x + 30 \right) = 2\) for the variable \(x\).
MathBot Answer:
The principal value in \(x > -30 - \frac{\pi}{2} \wedge x < -30 + \frac{\pi}{2} \wedge x \neq -30\) is \(x \approx -29.476401\)
The real solutions are: \[\begin{aligned}x &= \left\{-30 + \frac{65 \pi}{6} + 2 \pi n\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 4.0339203\; \middle|\; n \in \mathbb{Z}\right\}\\x &= \left\{\pi + 2 \pi n + \arctan{\left(\frac{1}{\tan{\left(30 + \frac{\pi}{3} \right)}} \right)}\; \middle|\; n \in \mathbb{Z}\right\} \approx \left\{6.2831853 n + 1.9395253\; \middle|\; n \in \mathbb{Z}\right\}\end{aligned}\]