sin5x - cos5x =√6/2 решить уравнение

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;