Question

Решить уравнение sin x + cos x = 1

Answer 1

возведем обе части в квадрат
(sinx+cosx)²=1
sin²x+2sinxcosx+cos²x=1
1+sin2x=1
sin2x=0
2x=πk, k∈Z
x=πk/2, k∈Z

Answer 2

2sin(x/2)cos(x/2)+cos²(x/2)-sin²(x/2)-sin²(x/2)-cos²(x/2)=0
2sin(x/2)cos(x/2)-2sin²(x/2)=0
2sin(x/2)*(cos(x/2)-sin(x/2))=0
sin(x/2)=0⇒x/2=πn⇒x=2πn,n∈z
cos(x/2)-sin(x/2)=0/cos(x/2)
1-tg(x/2)=0
tg(x/2)=1⇒x/2=π/4+πk⇒x=π/2+2πk,k∈z