Question

Решить систему уравнений

Answer 1

сложим
4cos(x-y)=2√3   cos(x-y)=√3/2
вычтем
4cos(x+y)=-2√2   cos(x+y)=-√2/2

x-y=+-π/6+2πk
x+y=+-3π/4+2πm
x=0.5(+-π/6+-3π/4)+π(k+m)
y=0.5(+-3π/4-+π/6)+π(m-k)   m;k∈Z

Answer 2

4sinxsiny=√3+√2
4cosxcosy=√3-√2
прибавим
4(cosxcosy+sinxsiny)=2√3⇒4cos(x-y)=2√3⇒cos(x-y)=√3/2⇒x-y=+-π/6
отнимем
4(cosxcosy-sinxsiny)=-2√2⇒4cos(x*y)=-2√2⇒cos(x+y)=-√2/2⇒x-y=+-3π/4
{x-y=-π/6
{x+y=-3π/4
2x=-11π/12⇒x=-11π/24⇒y=-11π/24+π/6=-7π/24
{x-y=-π/6
{x+y=3π/4
2x=7π/6⇒x=7π/12⇒y=3π/4-7π/12=π/6
{x-y=π/6
{x+y=-3π/4
2x=-7π/6⇒x=-7π/12⇒y=-3π/4+7π/12=-π/6
{x-y=π/6
{x+y=3π/4
2x=11π/12⇒x=11π/24⇒y=3π/4-11π/24=7π/24