Consider a real valued function $f$ such that $f(\sin(x)) + f(\cos(x)) = 2x - \frac{\pi}{2}$ Is there a way to find the range of $f(x)$?
I tried substituting $x$ as $\frac{\pi}{2}-x$, but that gives $x = \frac{\pi}{4}$ - which is a single value as opposed to a function. Is there a way to find out what the function is and its range?