Как решить 3sin^2 (x/2)+sin(x/2)*sin(pi/2-x/2)=2 - вопрос №38310963222222 от Muminat20022005 14.04.2020 21:38

Question

Алгебра: Как решить 3sin^2 (x/2)+sin(x/2)*sin(pi/2-x/2)=2

Muminat20022005 · Answer

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