The set of points of continuity of the function `f(x)= sqrt((1)/(2)-cos^(2)x)` is

Options

A. `{x: (pi)/(4)+2n pi le x le (3pi)/(4)+2n pi, n in I}`
B. `{x:(5pi)/(4)+2n pi le x le (7pi)/(4) +2n pi, n in I}`
C. `{x:(pi)/(4)+2n pi le x le (3pi)/(4)+2n pi } cup {x:(5pi)/(4)+2n pi le x le (7pi)/(4)+2n pi}`
D. None of the above

Answer

C

Explanation

The function f(x) is continuous at all points, where `(1)/(2) -cos^(2)x ge 0 rArr |cosx| le (1)/(sqrt(2))`
`rArr (pi)/(4)+2n pi le x le (3pi)/(4)+2 n pi `
`rArr (5pi)/(4) +2n pi le x le (7pi)/(4) + 2n pi, n in I`