Comprehension 2 (Q.No 4 to 6)
It is known that
`sqrt(tanx)+sqrt(cotx)={{:(sqrt(sinx)/sqrt(cosx)+sqrt(cosx)/sqrt(sinx), if 0ltxltpi/2),(sqrt(-sinx)/sqrt(cosx)+sqrt(-cosx)/sqrt(-sinx),if pi lt x lt (3pi)/(2)):}`
`d/(dx)(sqrt(tanx)-sqrt(cotx)) =1/2(sqrt(tanx)+sqrt(cotx))(tanx+cotx), AA in (0,pi,2) uu (pi,(3pi)/2)` and `d/(dx)(sqrt(tanx)+sqrt(cotx))=1/2(sqrt(tanx)-sqrt(cotx))(tanx+cotx), AA x in (0,pi/2) uu (pi, (3pi)/(2))`.
Value of the integral `I=int(sqrt(tanx)+sqrt(cotx))` dx, where `x in (0,pi/2)`, is

Options

A. `sqrt(2)sin^(-1)(cosx-sinx)+C`
B. `sqrt(2)sin^(-1)(sinx-cosx)+C`
C. `sqrt(2)sin^(-1)(sinx+cosx)+C`
D. `-sqrt(2)sin^(-1)(sinx+cosx)+C`

Explanation

A