Write the maximum and minimum values of sin (sin x).

sin(x) has maximum value at x = π/2 and its minimum at

x = -π/2 which are 1 and -1 respectively.

As 1 < π/2;

so, the argument of the outer sin always lies within the interval

[-π/2, π/2]

So the maximum and minimum of the given function are

sin 1 and - sin 1.