Question

решить неравенства: sin^2 x/2-cos^2 x/2≥1/2; 4 sin 2x cos2x>√3:​

Answer 1

sin^2(x/2)-cos^2(x/2)>=1/2

-cosx>=1/2

cosx<=-1/2

[2П/3+2Пk;4П/3+2Пk]

2*2*sin2x*cos2x>√3

2sin4x>√3

sin4x>√3/2

П/3+2Пk<=4x<=2П/3+2Пk

П/12+Пk/2<=x<=П/6+Пk/2