P can complete five-eighths of a work in 15 days and Q can complete three-fourths of the same work in 30 days. They worked together for 8 days and then P left. How much time will Q working alone, take to complete the remaining work?
If \(tan\space \theta-cot\space \theta = cosec\space \theta\), \(0^0<\theta<90^0\), then what is the value of \({2tan\space \theta-cos\space \theta\over \sqrt3cot\space \theta+sec\space \theta}\) ?