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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.

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  • $\begingroup$ Maybe Lagrange multiplayer could help? $\endgroup$ – Vim May 12 '15 at 6:42
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    $\begingroup$ $(2\sin x+1)(2\cos y+1)=0$ $\endgroup$ – Mann May 12 '15 at 6:42
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    $\begingroup$ Are we constraining $x,y$ to $[0,2\pi].$ Otherwise there is no bound for $x+y$ for this curve. $\endgroup$ – matt biesecker May 12 '15 at 6:44
  • $\begingroup$ @Mann you should place this in the answer action. Nice. $\endgroup$ – Moti May 12 '15 at 6:52
  • $\begingroup$ 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 $x,y \in \left[0,2\pi\right]$ $\endgroup$ – Mann May 12 '15 at 6:54
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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

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  • $\begingroup$ Could you improve the formatting of your answer by using MathJaX? Maybe add a sentence or two to explain what you are doing? $\endgroup$ – Hrodelbert May 12 '15 at 8:20

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