Пожалуйста, помогите с тригонометрией, 10 класс sin²x/4 - cos²x/4 = 1 sin2xcos2x=-1/4 sin3xcosx-cos3xsinx=√3/2 sin x/3cos π/5 - cos x/3sin π/5=√2/2 sin²x-sin2x=0
Sin²x/4-cos²x/4=1 -(cos²x/4-sin²x/4)=1 cosx/2=-1 x/2=π+2πn x=2π+4πn n∈Z sin2xcos2x=-1/4 2sin2xcos2x/2=-1/4 sin4x=-1/2 4x=(-1)^n×arcsin(-1/2)+πn arcsin(-1/2)=-π/6 4x=(-1)^n×(-π/6)+πn x=(=1)^n+1×π/24+π/4n n∈Z sin3xcosx-cos3xsinx=√3/2 sin(3x-x)=√3/2 sin2x=√3/2 2x=(-1)^n×arcsin√3/2+πn arcsin√3/2=π/3 2x=(-1)^n×π/3+πn x=(-1)^n×π/6+πn/2 n∈Z sinx/3cosπ/5-cosx/3sinπ/5=√2/2 sin(x/3-π/5)=√2/2 x/3-π/5=(-1)^n×arcsin√2/2+πn arcsin√2/2=π/4 x/3-π/5=(-1)^n×π/4+πn x/3=(-1)^n×π/4+π/5+πn x=(-1)^n×3π/4+3π/5+3πn n∈Z sin²x-sin2x=0 sin²x-2sinxcox=0 sinx(sinx-2cosx)=0 sinx=0 sinx-2cosx=0 |:cosx x=πn tgx-2=0 tgx=2 x=arctg2+πn n∈Z
Спасибо.