Question

Sin20x+10cos10x=0 в интервале(9,4;9,7)

Answer 1

Решение
sin2*(10x) + 10*cos10x = 0
2 sin10x*cos10x + 10cos10x = 0
2*cos10x*(sin10x + 5) = 0
cos10x = 0
10x = π/2 + πn, n∈Z
x = π/20 + πn/10 + πn, n∈Z
sin10x - 5 = 0
sin10x = - 5, не удовлетворяет условию: I sinx I ≤ 1
Ответ: x = π/20 + πn/10 + πn, n∈Z