sin^3x+sinx*sin2x-3 sin x*cos^x-6 cos^3x=0
sin2x=2sinxcosx ⇒
sin³x+2sin²xcosx-3sinxcos²x-6cos³x=0
Делим ур-ие на cos³x≠0
tg³x+2tg²x-3tgx-6=0
tg²x(tgx+2)-3(tgx+2)=0
(tgx+2)(tg²x-3)=0, (tgx+2)(tgx-√3)(tgx+√3)=0
a) tgx=-2, x= -arctg2+πn, n∈Z
b) tgx=√3, x=π/3+πk, k∈Z
c) tgx=-√3, x= -π/3+πm, m∈Z
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Verified answer
sin2x=2sinxcosx ⇒
sin³x+2sin²xcosx-3sinxcos²x-6cos³x=0
Делим ур-ие на cos³x≠0
tg³x+2tg²x-3tgx-6=0
tg²x(tgx+2)-3(tgx+2)=0
(tgx+2)(tg²x-3)=0, (tgx+2)(tgx-√3)(tgx+√3)=0
a) tgx=-2, x= -arctg2+πn, n∈Z
b) tgx=√3, x=π/3+πk, k∈Z
c) tgx=-√3, x= -π/3+πm, m∈Z