18.29
а) 3sin²2x-2sin²2x-2cos²2x-sin2x·cos2x=0
sin²2x-sin2xcos2x-2cos2x=0 Поделим на cos²2x
tg²2x-tg2x-2=0
tg2x=a
a²-a-2=0
a=2 или a=-1
tg2x=2⇒2x=arctg2+πn⇒x=(arctg2+πn)/2
tg2x=-1⇒2x=-π/4+πn⇒x=-π/8+πn/2
18.30
a) 4sin²x/2-3sin²x/2-3cos²x/2-2sinx/2·cosx/2=0
sin²x/2-3cos²x/2-2sinx/2·cosx/2=0
tg²x/2-2tgx/2-3=0
a²-2a-3=0
a=3 или a=-1
tgx/2=3⇒x/2=arctg3+πn⇒x=2(arctg3+πn)
tgx/2=-1⇒x/2=-π/4+πn⇒x=-π/2+2πn