Question

1)sinxsiny=1/a cosxcosy=1/b 2)cosx+cosy=дробь3/c x+y=p/3 решите уравнение

Answer 1

sinxsiny=1/a      cosxcosy=1/b
сos(x-y)-cos(x+y)= 2/a
сos(x-y)+cos(x+y)=2/b
2сos(x-y)=2/a+2/b    cos(x-y)=(a+b )/ab     x-y=+- arccos[(a+b )/ab]+2πk
2cos(x+y)=2/b-2/a     cos(x+y)=(a-b )/ab    x+y= +-arccos[(a-b )/ab]+2πm
x=+-0.5arccos[(a+b )/ab]+-0.5arccos[(a-b )/ab]+π(k+m)
y=+-0.5arccos[(a-b )/ab]+-0.5arccos[(a+b )/ab]+π(m-k)   m,k∈Z