Question

Resolva a equação sen x + sen y = 1, sabendo que x + y = π/3

Urgente!

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Answer 1

• Use que:

sen(x) + sen(y) = 2 . sen[(x + y)/2] . cos[(x - y)/2]

• Desenvolva:

2 . sen[(x + y)/2] . cos[(x - y)/2] = 1

2 . sen((π/3)/2) . cos[(x - y)/2] = 1

2 . sen(π/6) . cos[(x - y)/2] = 1, sen(π/6) = 1/2

cos[(x - y)/2] = 1 e cos(0) = 1

Então:

[(x - y)/2] = 0

x - y = 0

x + y = π/3

2x = π/3

x = π/6 + k2π

π/6 + k2π + y = π/3

y = π/6 - π/6 - k2π

y = π/6 - k2π

Resposta:

x = π/6 + k2π

y = π/6 - k2π