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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!