Relations and Functions

Find period of $$\dfrac{{1 + \sin x}}{{\cos x\left( {1 + cosecx} \right)}}$$
The diagram shows a triangle ABC.
Mark the point of intersection of the two loci with the letter D.
Give an example of a relation which is symmetric only.
Show that the set G of all positive rationals forms a group the compositions * defined by $$a*b = \frac{{ab}}{3}$$ for all $$a,b \in G$$
The number of one-one and onto functions that can be defined from { 1,2,3,4 } onto set  is 24  then n ( B ) is