So im currently trying to find the extremas of the function $f(x,y) = \cos(x+y) + \sin(x) + \sin(y)$
I've already computed the partial derivatives:
$$ f_x(x,y) = \cos(x) - \sin(x+y)\\ f_y(x,y) = \cos(y) - \sin(x+y) $$ But now i am stuck at solving for the stationary points: $$ 0 = \cos(x) - \sin(x+y)\\ 0 = \cos(y) - \sin(x+y) $$ It would be very nice if someone could help me with this
Hint: $$\cos a=\sin b\iff\cos a=\cos\left(\frac\pi2-b\right)$$ $$\iff a\equiv\pm\left(\frac\pi2-b\right)\bmod{2\pi}.$$