If 4sinx.cosy+2sinx+2cosy+1=0 where x,y ∈ [0,2pie]. Find largest possible value of the sum (x+y).


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Question Number 29491 by math solver last updated on 09/Feb/18

$I f 4 s i n x . c o s y + 2 s i n x + 2 c o s y + 1 = 0$ $w h e r e x, y \in [0, 2 p i e] . F i n d l a r g e s t$ $p o s s i b l e v a l u e o f t h e s u m (x + y) .$
	Answered by ajfour last updated on 09/Feb/18

	$(1 + 2 \sin x) (1 + 2 \cos y) = 0$ $\Rightarrow \sin x = - \frac{1}{2}; \cos y = w h a t e v e r$ $o r \cos y = - \frac{1}{2}; \sin x = w h a t e v e r$ $i n t h i s c a s e$ ${(x + y)}_{m a x} = 2 π + (π + \frac{π}{3}) = \frac{10 π}{3}$ $u n d e r f i r s t c a s e$ ${(x + y)}_{m a x} = (2 π - \frac{π}{6}) + 2 π = \frac{23 π}{6}$ $H e n c e {(x + y)}_{m a x} = \frac{23 π}{6} .$
	Commented by math solver last updated on 09/Feb/18

	$t h a n k y o u s i r .$
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