I have got a problem and I would appreciate if one could help.
I have to maximise following function that is the sum of sine/cosine functions:
$$ f(x,y)=a_1 \cos(x) +b_1 \sin(x)+ a_2 \cos(y) +b_2 \sin(y)+ a_3 \cos(y-x) +b_3 \sin(y-x) $$ and find the $x$ and $y$ values where the function $f(x,y)$ is maximised assuming that $ 0\leq x,y<2\pi$. I am aware that I can do first derivative and find the $x$ and $y$. however, I am wondering if one can think of simpler way of maximising this function.
I have realized that for $x=y=0$, the cos functions are maximized and for $x=y=\pi/2$ the sine functions reach max. so, this function is concave in $0<x,y<\pi/2$.