as we know,
quantity under square root should be either positive or zero to be defined
hence sin x –1 should be positive or zero
but sin x can’t be more than 1.
hence it can not be positive but it can be zero where sin x = 1
hence only solution for this function to be defined is sin x = 1
hence x = (2n + 1)

/2
thus domain = (2n + 1)

/2 ; where n = integer