Решить систему : x-y=П/2 sinx+siny=√2

Question

Решить систему :
x-y=П/2
sinx+siny=√2

Answer 1

X-y=П/2
sinx+siny=√2
2sin[(x+y)/2]*cos[(x-y)/2]=√2
2sin[(x+y)/2]*cosπ/4=√2
2*√2/2*sin[(x+y)/2]=√2
sin[(x+y)/2]=1
(x+y)/2=π/2
x+y=π
x-y=π/2
2x=3π/2
x=3π/4
y=π/4