The set of values of x satisfying `["sin"("cos" x)] =-1` is `([.]` denotes the greatest integer function)

Options

A. `((4n + 1) pi, (4n + 3) pi), n in Z`
B. `[(n + 1) (pi)/(2), (4n +3)(pi)/(2)], n in Z`
C. `((4n + 1)(pi)/(2), (4n + 3)(pi)/(2)), n inZ`
D. none of these

Answer

C

Explanation

We have,
`["sin" ("cos"x)] = -1`
`rArr -1 le "sin" ("cos"x) lt 0`
`rArr "cos" x lt 0`
`rArr x in ((4n + 1)(pi)/(2), (4n + 3)(pi)/(2)), n inZ`