Question

Find the interval of the monotonocity of the function f(x) = sin(sinx) + cos(sinx) in (0, π).

Answer 1

Let g(x) = sinx + cosx and h(x) = sinx

Now, g'(x) = cosx – sinx

Thus, f(x) is strictly increases in (0, π/2) and strictly decreasing in (π/4 , π).