Question

Решите тригонометрическое уравнение: Sin5x-sin3x=cos4x

Answer 1

sin5x - sin3x = cos4x

2*sin[(5x - 3x)/2]*cos[(5x + 3x)/2] = cos4x

2sinx*cos4x = cos4x

2sinx*cos4x - cos4x = 0

cos4x(2sinx - 1) = 0

cos4x = 0 или 2sinx - 1 = 0

cos4x = 0 или sinx = 1/2

4x = π/2 + πn, n ∈ Z; x = (-1)ⁿπ/6 + πn, n ∈ Z

x = π/8 + πn/4, n ∈ Z; (-1)ⁿπ/6 + πn, n ∈ Z

ответ: x = π/8 + πn/4; (-1)ⁿπ/6 + πn, n ∈ Z.