Question 69
a) Does there exist a function $f : \mathbb{R} \to \mathbb{R}$, such that for any real $x$ the following equality holds $f(\sin x) + f(\cos x) = 2$?
b) The same question for $f(\sin x) + f(\cos x) = \sin 2x$.
b) The same question for $f(\sin x) + f(\cos x) = \sin 2x$.