Question

как решить 3sin^2 (x/2)+sin(x/2)*sin(pi/2-x/2)=2

Answer 1

3sin²(x/2)+sin(x/2)*cos(x/2)-2sin²(x/2)-2cos²(x/2)=0
sin²(x/2)+sin(x/2)cos(x/2)-2cos²(x/2)=0 (/cos²x/2≠0
(sin(x/2)/cos(x/2))²+sin(x/2)/cos(x/2)-2=0
tg²x/2+tgx/2-2=0
tgx/2=t
t²+t-2=0
t=1  t=-2
tgx/2=1                tgx/2=-2
x/2=π/4+πn            x/2=-arctg2+πn
x=π/2+2πn             x=-2arctg2+2πn