Two aeroplanes leave an airport, one after the other. After moving on the runway, one flies due north and the other flies due south. The speeds of the two aeroplanes are \(400 \ km/h\) and \(500 \ km/h\) respectively. Considering \(PQ\) as the runway and \(A\) and \(B\) are any two points on the path followed by two planes, then answer the following questions.
1. Determine \(\tan \theta\) if \(\angle APQ = \theta\).
2. Find \(\cot \)\(C\).
3.\(\text{cosec}^2 \theta - 1\)
4. \(\cot^2 \theta\)