Question 50
a) Does there exist a function $f: \mathbb{R} \to \mathbb{R}$, such that for any real $x$ the following equality holds $f(\sin x) + f(\cos x) = 1$?
b) The same question for $f(\sin x) + f(\cos x) = \sin x$.
(I. Gorodnin)
b) The same question for $f(\sin x) + f(\cos x) = \sin x$.
(I. Gorodnin)