For a fixed real number k with ∣k∣<1, define the function
F(x)=arcsin(kx)+arccos(kx)
with domain ∣kx∣≤1.
(a) Show that F′(x)=0 for every x in the domain.
(b) Compute F(0) and thus determine the constant value taken by F(x) for all admissible x. Explain your reasoning clearly.