The maximum value of sin x is 1 and minimum value of sin x is -1

Now, x = -90,

then sin(sin x) = sin{sin (-90)}

                      = sin{-sin (90)}

                      = sin(-1)

                     = -sin 1

So, Minimum value of sin(sin x) is -sin 1 when x = -90

Again, when, x = 90,

then sin(sin x) = sin{sin 90}

                      = sin(1)

                     = sin 1

So, Maximum value of sin(sin x) is sin 1 when x = 90