Answer:
To solve the equation \(\sin(x) \tan(x-30^\circ) = 0\) for \(0^\circ \leq x \leq 360^\circ\), you need to consider the cases where either \(\sin(x) = 0\) or \(\tan(x-30^\circ) = 0\).
1. **Case 1: \(\sin(x) = 0\)**
\(\sin(x) = 0\) when \(x = 0^\circ\) or \(x = 180^\circ\).
2. **Case 2: \(\tan(x-30^\circ) = 0\)**
\(\tan(x-30^\circ) = 0\) when \(x - 30^\circ = n \times 180^\circ\) where \(n\) is an integer.
Solve for \(x\) in this case: \(x = 30^\circ + n \times 180^\circ\).
Combine the solutions from both cases, and ensure they are within the given range \(0^\circ \leq x \leq 360^\circ\).
