The solution set of the inequation `"cos" x - "sin" xge 1 "in" [0, 2pi]`, is

Options

A. `[0, pi//4] cup [7 pi//4, 2pi]`
B. `[3 pi//2, 7 pi//4] cup {0}`
C. `[3 pi//2, 2pi] cup {0}`
D. none of these

Answer

C

Explanation

We have,
`"cos"x - "sin" x ge 1`
`rArr (1)/(sqrt(2)) "cos" x- (1)/(sqrt(2)) "sin"x ge (1)/(sqrt(2))`
`rArr "cos"x "cos" (pi)/(4) -"sin" x"sin"(pi)/(4) ge (1)/(sqrt(2))`
`"cos" (x + (pi)/(4)) ge (1)/(sqrt(2)) rArr x in [3 pi//2, 2 pi] cup {0}`