Решите уравнение : 2 cos5a cos8a=cos 13a

Question

Решите уравнение :
2 cos5a cos8a=cos 13a

Answer 1

2cos5αcos8α=cos13α;

cos(5α + 8α) + cos(5α - 8α) = cos13α;

cos13α + cos3α = cos13α;

cos3α = 0

3α = π/2 + πn, n ∈ Z

α = π/6 + πn/3, n ∈ Z

Ответ: π/6 + πn/3, n ∈ Z.