Question

Помогите пожалуйста
П-4(1 столбик)
П-6(полностью)

Answer 1

П-4
1)sinx+sin5x-√2sin3x=0
2sin3xcos2x-√2sin3x=0
sin3x(2cos2x-√2)=0
sin3x=0⇒3x=πn⇒x=πn/3,n∈Z
cos2x=√2/2⇒2x=+-π/4+2πk⇒x=+-π/8+πk,k∈Z
3)1/2[cos(70+x-x+20)+cos(70+x+x-20)]=1/2
cos90+cos(2x+50)=1
cos(2x+50)=1
2x+50=360n⇒2x=-50+360n⇒x=-25+180n,n∈Z
5)4cos²x+sinxcosx+3sin²x-3sin²x-3cos²x=0
sinxcosx+cos²x=0/cos²x≠0
tgx+1=0
tgx=-1
x=-π/4+πn,n∈Z
6)cos²x-3sinxcosx+sin²x+cos²x=0
sin²x-3sinxcosx+2cos²x=0/cos²x≠0
tg²x-3tgx+2=0
tgx=a
a²-3a+2=0
a1+a2=3 U a1*a2=2
a1=1⇒tgx=1⇒x=π/4+πn,n∈Z
a2=2⇒tgx=2⇒x=arctg2+πk,k∈Z
П-6
1)2sin²(x+3π/2)≥1
2cos²x≥1
2(1+cos2x)/2≥1
1+cos2x≥1
cos2x≥0
-π/2+2πn≤2x≤π/2+2πn,n∈Z
-π/4+πn≤x≤π/4+πn,n∈Z
x∈[-π/4+πn;π/4+πn,n∈Z]
2)ctg3x-√3≥0
ctg3x≥√3
πn<3x≤π/6+πn,n∈Z
πn/3<x≤π/18+πn/3,n∈Z
x∈(πn/3;π/18+πn/3,n∈Z]