The value of \(\sqrt{cosec\theta-cot\theta\over cosec\theta+cot\theta}\)\(\div {sin\theta\over1+cos\theta}\) is equal to :

In a triangle ABC, right-angled at C, if \(sec A={13\over5}\), then find the value of \(\frac{1+ \sin A}{\cos B}\).

To do a certain work, the ratio of efficiency of A to that of B is 3 : 7. Working together, they can complete the work in \(10\frac{1} {2} \)days. They work together for 8 days. 60% of the remaining work will be completed by A alone in:

A man, a woman and a boy can complete a work in 3, 4 and 12 days, respectively. How many boys must assist one man and one woman to complete the same work in one day?