Question

Решите систему: X+У=pi/3 sinx*siny=1/4

Answer 1

X+У=π/3,  y= π/3 -x
sinx·siny=1/4
sinx·sin( π/3-x)=0,5cos(x-( π/3-x)-
-cos(x+ π/3-x)=1/4
0,5(cos(2x-( π/3)-cos( π/3) )=1/4
0,5 cos(2x-( π/3) -0,25=0,25,
0,5 cos(2x-( π/3)=0,5,  cos(2x-( π/3)=1
2x- π/3 = 2πn,2x=2πn+  π/3 ,
x=  πn  +  π/6,y=   π/3- πn - π/6= π/6  - πn 
Ответ(  πn  +  π/6 ; π/6 - πn),где  n  целое число.