Cos (x) + √3sin (x) = 1

Question

Алгебра

Николаич

20 августа, 23:03

Cos (x) + √3sin (x) = 1

+4

Ответы (2)

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Иваныч · 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;

Евдения · 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