Sin a + cos b =√2 sin b + cos a =√2 Найти sin(a+b) и cos(a+b)

Question

Sin a + cos b =√2 sin b + cos a =√2 Найти sin(a+b) и cos(a+b)

Answer 1

Sina+cosb=√2

sinb+cosa=√2

sin(a+b)=?;cos(a+b)=?

1)sin(a+b)=sinacosb+cosasina
(sina+cosb)²=2
+
(sinb+cosa)²=2
sin²a+2sinacosb+cos²b+sin²b+2sinbcosa
+cos²a=4
2+2(sinacosb+cosasinb)=4
sinacosb+cosasinb=1
sin(a+b)=1
a+b=π/2+2πk;k€z
2)cos(a+b)=0