Cos(x) + √3sin(x) = 1

Question

Cos(x) + √3sin(x) = 1

Answer 1

Cos(x) + √3sin(x) =1;
2(1/2 cos(x) + √3/2 sin(x)) =1;
sin(π/6)cos(x) + sin(x)cos(π/6) = 1/2;
1/2 (sin(π/6+x) + sin(π/6-x) + sin(π/6+x) + sin(x-π/6) = 1/2;
2sin(π/6+x)=1;
sin(π/6+x)=1/2;
π/6+x = (-1)ⁿπ/6 + πn, n∈Z;
x = (-1)ⁿπ/6 -π/6 +πn, n∈Z;
Ответ: x = (-1)ⁿπ/6 -π/6 +πn, n∈Z;

Answer 2

2(1/2*сosx+√3/2*sinx)=1
sin(π/6+x)=1
π/6+x=π/2+2πk
x=-π/6+π/2+2πk
x=π/3+2πk,k∈z