Question

I will state the question exactly as it is:

Answer 1

If \(x,y \in [0, \pi/2)\):\[\sin^4 x + \cos^4 y + 2 = 4\sin x \cos y\]Then find the value of:\[\sin x + \sin y \]...
The answer is given as 2.

Answer 2

@Mehek14 @pinkbubbles

Answer 3

I have two issues with this: one, \(\pi/2\) is not included. If I acknowledge this as a small mistake, even then, if \(\sin x + \sin y = 2\), then \(x = y = \pi/2\). But of course this does not satisfy the condition.

Here is what *does* satisfy the condition: \(x = 0;~ y = \pi/2\)

Answer 4

@ganeshie8

Answer 5

@ikram002p @dan815

Answer 6

@SolomonZelman

Answer 7

@oldrin.bataku of course.

Answer 8

Oops, I meant that \(y = 0; x = \pi/2\) satisfies the condition. Moving on...

Answer 9

Pi/2 MUST be included.

Answer 10

I've solved the question thoroughly nd m sure that pi/2 mst be included.

Answer 11

Even then, the answer couldn't be 2, right?

Answer 12

Also, how did you solve this question thoroughly if you don't mind explaining?

Answer 13

K wait lemme switch on my laptop :)

Answer 14

Did you solve this my maxima-minima or ...?

Answer 15

No i jst simplified the expression

Answer 16

Oh, great.

Answer 17

Yeah, that's what I got too... finally.

Answer 18

Thank you!

Answer 19

So the answer isn't 2, it's 1, right?

Answer 20

The question asked for sin x + sin y...

Answer 21

yes its one :)

Answer 22

Cool, I was wondering where the mistake was in my work. There wasn't any. I'll report this, thanks!

Answer 23

ur welcome :)