If-4sinx-cosy-2sinx-2cosy-1-0-where-x-y-0-2pie-Find-largest-possible-value-of-the-sum-x-y-

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 .