Question

Решите тригонометрическое уравнение : sin5x + cos5x = 0​

Answer 1

Ответ:

sin5x-cos5x=√6/2;⇔

(sin5x-cos5x)²=6/4;⇒sin²5x-2sin5x·cos5x+cos²5x=6/4;⇒

1-sin10x=6/4;⇒sin10x=-1/2;⇒

10x₁=-π/6+2kπ;k∈Z;x₁=-π/60+kπ/5;k∈Z;

10x₂=7π/6+2kπ;k∈Z;x₂=7π/10+kπ/5;k∈Z;

Объяснение: