Question

sin5x - cos5x =√6/2 решить уравнение

Answer 1

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;