The probability that `sin^(-1)(sinx)+cos^(-1)(cosy)` is an integer `x,y in {1,2,3,4}` is

Options

A. `(1)/(16)`
B. `(3)/(16)`
C. `(15)/(16)`
D. `(14)/(16)`

Answer

B

Explanation

`(b)` For expression `sin^(-1)(sinx)+cos^(-1)(cosy)` to be an integer, `x` should lie between `[-(pi)/(2),(pi)/(2)]` and `y` should lie between `[0,pi]`
`x=1` and `y=1,2,3`
`:.` Required probability `=(1/4)(3/4)=(3)/(16)`