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П-4(1 столбик)
П-6(полностью)

П-41)sinx+sin5x-√2sin3x=02sin3xcos2x-√2sin3x=0sin3x(2cos2x-√2)=0sin3x=0⇒3x=πn⇒x=πn/3,n∈Zcos2x=√2/2⇒2x=+-π/4+2πk⇒x=+-π/8+πk,k∈Z3)1/2[cos(70+x-x+20)+cos(70+x+x-20)]=1/2cos90+cos(2x+50)=1cos(2x+50)=12x+50=360n⇒2x=-50+360n⇒x=-25+180n,n∈Z5)4cos²x+sinxcosx+3sin²x-3sin²x-3cos²x=0sinxcosx+cos²x=0/cos²x≠0tgx+1=0tgx=-1x=-π/4+πn,n∈Z6)cos²x-3sinxcosx+sin²x+cos²x=0sin²x-3sinxcosx+2cos²x=0/cos²x≠0tg²x-3tgx+2=0tgx=aa²-3a+2=0a1+a2=3 U a1*a2=2a1=1⇒tgx=1⇒x=π/4+πn,n∈Za2=2⇒tgx=2⇒x=arctg2+πk,k∈ZП-61)2sin²(x+3π/2)≥12cos²x≥12(1+cos2x)/2≥11+cos2x≥1cos2x≥0-π/2+2πn≤2x≤π/2+2πn,n∈Z-π/4+πn≤x≤π/4+πn,n∈Zx∈[-π/4+πn;π/4+πn,n∈Z]2)ctg3x-√3≥0ctg3x≥√3πn<3x≤π/6+πn,n∈Zπn/3<x≤π/18+πn/3,n∈Zx∈(πn/3;π/18+πn/3,n∈Z]