In the diagram above, Ox and Oy are the rectangular axes and the straight line PAQ passes through the fixed point A ( 4,1 ). The angle QPO= Theta and 0 < Theta < pi/2

Let T = theta ( Sorry , I do not know how to insert the symbol, I tried &Theta but no luck )

a) Show thatOP + OQ = 5 + 4 tan T + cot T and show that as T changes, the least value of OP + OQ is 9.

b) Show that PQ = 4 sec T + cosec T and find, correct to two significant figures, the minimum value of Q when T changes.