Cos(p/2+x)cos x + sin(p/2+x)sin x =0

Question

Алгебра: Cos(p/2+x)cos x + sin(p/2+x)sin x =0

iskakova2000 · Accepted Answer

1) 2sin(x/2)=3sin²(x/2) 2sin(x/2)-3sin²(x/2)=0 sin(x/2) (2-3sin(x/2))=0 a) sin(x/2)=0 x/2=πk, k∈Z x=2πk,  k∈Z b)  2-3sin(x/2)=0 -3sin(x/2)=-2 sin(x/2)=2/3 x/2=(-1)^n * arcsin(2/3)+πk,  k∈Z x=2*(-1)^n * arcsin(2/3)+2πk,  k∈Z ответ: 2πk,  k∈Z;             2*(-1)^k*arcsin(2/3)+2πk, k∈Z. 2) sin6xcosx+cos6xsinx=0.5 sin(6x+x)=0.5 sin7x=0.5 7x=(-1)^k*(π/6)+πk,  k∈Z x=(-1)^k*(π/42)+(π/7)*k,  k∈Z ответ: (-1)^k*(π/42)+(π/7)*k,  k∈Z. 3) 3sinx+4sin(π/2+x)=0 3sinx+4cosx=0 =0 a) При у=-1/2 , k∈Z; b)  При у=2...

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