1) 2sin2x+11/2 *(2sinx cosx)+12cos2x=0
2sin2x+11/2 sin2x+12cos2x=0
15sin2x +12cos2x=0; 5sin2x+4cos2x=0; cos2x≠0
5tg2x+4=0; tg2x=-0,8; 2x=arctg(-0,8)+πn
x=-0,5arctg0,8+0,5πn
2)4tgx-14*(1/tgx)+1=0; tgx≠0
4tg^2 x+tgx-14=0
t=tgx; 4t^2+t-14=0; D=1+4*4*14=225=15^2; t1=(-1-15)/8=-2; t2=7/4
tgx=-2 ili tgx=7/4
x=-arctg2+πn x=arctg1,75+πk
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3)cos2x=cos^2x-1; sin2x=2sinx cosx
8sinx cosx+10*(2cos^2 x-1)=1
8sinx cosx+20cos^2 x-11*(sin^2 x+cos^2 x)=0
-11sin^2+8sinxcosx +9cos^2x=0; /cos^2 x≠0
-11tg^2 x+8tgx+9=0; y=tgx; -11y^2+8y+9=0; D1=16+99? y2=-4-√Д1)/(-11