# Find largest possible value of $x+y$

If $4\sin x. \cos y + 2\sin x+2\cos y+1=0$, find the largest possible value of the sum $(x+y)$. How do I manipulate my expression? I am not getting $(x+y)$ form. Thanks.

• Maybe Lagrange multiplayer could help? – Vim May 12 '15 at 6:42
• $(2\sin x+1)(2\cos y+1)=0$ – Mann May 12 '15 at 6:42
• Are we constraining $x,y$ to $[0,2\pi].$ Otherwise there is no bound for $x+y$ for this curve. – matt biesecker May 12 '15 at 6:44
• @Mann you should place this in the answer action. Nice. – Moti May 12 '15 at 6:52
• Naa, it's ok It would be too small anyway. :) The answer seems to be $\frac{23\pi}{6}$ where $y=2\pi$ and $x=\frac{11 \pi}{6}$ $\forall$ value of $x,y \in \left[0,2\pi\right]$ – Mann May 12 '15 at 6:54

As Shown by Mann (2sinx+1)(2cosy+1)=0 Maximum value of x+y occurs when both expressions are 0 x+y=11.$\pi$/6 + 4.$\pi$/6=15.$\pi$/6