If sin^4 x + cos^4 y + 2 = 4 sinx.cosy & 0 ≤ x,y ≤ (π/2) , then the value of sinx + cosy is equal to


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Question Number 23304 by Tinkutara last updated on 28/Oct/17

$If \sin^{4} x + \cos^{4} y + 2 = 4 sinx . cosy &$ $0 ⩽ x, y ⩽ \frac{π}{2}, then the value of \sin x +$ $\cos y is equal to$
Commented by Joel577 last updated on 28/Oct/17

${W h a t}^{'} s t h e n a m e o f u r b o o k ?$
Commented by Joel577 last updated on 28/Oct/17

$O w h, I t h i n k i t w a s f r o m u r t e x t b o o k .$ $B e c a u s e u h a v e a s k e d s o m a n y q u e s t i o n s$ $I w o n d e r h o w m a n y a s s i g n m e n t s d i d u g e t f r o m s c h o o l$ $e v e r y d a y$
	Answered by ajfour last updated on 28/Oct/17

	$l e t \sin x + \cos y = S$ $\sin x - \cos y = D$ $\sin x \cos y = P$ $T h e n w h a t i s g i v e n c o n v e r t s t o$ ${(\sin^{2} x - \cos^{2} y)}^{2} + 2 \sin^{2} x \cos^{2} y + 2$ $= 4 \sin x \cos y$ $\Rightarrow S^{2} D^{2} + 2 P^{2} + 2 - 4 P = 0$ $\Rightarrow S^{2} D^{2} + 2 {(P - 1)}^{2} = 0$ $S c a n n o t b e z e r o f o r 0 ⩽ x, y ⩽ \frac{π}{2}$ $S o D = 0 a n d P = 1$ $\Rightarrow \sin x = \cos y a n d \sin x \cos y = 1$ $t h i s c a n b e t r u e o n l y i f$ $x = \frac{π}{2} a n d y = 0$ $S o \sin x + \cos y = 2 .$
	Commented by Tinkutara last updated on 29/Oct/17

	$Thank you very much Sir!$
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