Find (x,y) pairs that satisfy sin 2 </msup> &#x2061;<!-- ⁡ --> x +

Laila Andrews

Laila Andrews

Answered question

2022-05-13

Find (x,y) pairs that satisfy sin 2 x + sin 2 y = sin x + sin y with 0 x , y π / 2?

Answer & Explanation

frogoogg31

frogoogg31

Beginner2022-05-14Added 12 answers

For every t [ 0 , π 2 ] : sin ( t ) sin 2 ( t ) 0
Hence, for every ( x , y ) [ 0 , π 2 ] 2 :
sin ( x ) sin 2 ( x ) + sin ( y ) sin 2 ( y ) = 0 ( sin ( x ) = sin 2 ( x ) a n d sin ( y ) = sin 2 ( y ) )
Finally, solutions are (0,0), ( π 2 , 0 ), ( 0 , π 2 ) and ( π 2 , π 2 ).
Jayla Faulkner

Jayla Faulkner

Beginner2022-05-15Added 6 answers

Hint: sin 2 x sin x , sin 2 y sin y sin 2 x = sin x , sin 2 y = sin y

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