B1
2<span>√3*cos60*sin90=2<span>√3*1/2 * 1 = <span>√3
</span></span></span>ctg30 * tg45 = <span>√3 * 1 = <span>√3
</span></span><span>√3/<span>√3=1
</span></span>B2
4sin(-п/3)cos(-п/6)=-4sin(п/3)сos(п/6)=-4*<span>√3/2 * <span>√3/2 = -4*3/4 = -3
</span></span>2tg(-п/3) - сtg(-п/6) = -2tg(п/3)+сtg(п/6) = -2<span>√3+<span>√3 = -<span>√3
</span></span></span>-<span>√3/<span>√3=-1
</span></span>-3-1=-4
В3
-1<span>≤cosx<span>≤1
</span></span>0<span>≤cos^2(x)<span>≤1
</span></span>2<span>≤cos^2(x)+2<span>≤3
</span></span>2+3=5
В4
sin(7п/6) - cos(п/8) = -1/2 - сos(п/8)
п/8 - это первая четверть, косинус положительный, значит разность -1/2-cos(п/8) отрицательная, значит sin(7п/6)-сos(п/8)<0. Значит модуль раскроется со знаком минус. В итоге результат будет равен -1
В5
sin(2arcctg(-1)-п) =sin(2(п-arcctg1)-п)=sin(2(п-п/4)-п)=sin(2*3п/4-п)=sin(3п/2 - п) =sin(п/2)=1
В6
sin^2(b) - tg^2(b) = sin^2(b) - sin^2(b)/cos^2(b) = sin^2(b)*(1-1/cos^2(b) = sin^2(b)*(cos^2(b)-1)/cos^2(b) = sin^2(b)*(-sin^2(b))/cos^2(b)=-sin^4(b)/cos^2(b)
cos^2(b)-ctg^2(b)=cos^2(b)-cos^2(b)/sin^2(b)=cos^2(b)*(1-1/sin^2(b) = cos^2(b) * (sin^2(b)-1)/sin^2(b) = cos^2(b)* (-cos^2(b)/sin^2(b) = -cos^4(b)/sin^2(b)
-sin^4(b)/cos^2(b) : (-cos^4(b)/sin^2(b)) = sin^4(b)/cos^2(b) * sin^2(b)/cos^4(b) = sin^6(b)/cos^6(b) = tg^6(b)
tg^6(b)-tg^6(b)=0
B7
ctga=1/7 => 1/tga=1/7 => tga=7
(5sina-2cosa)/(2cosa+5sina) = (5tga - 2)/(5tga+2) = (35-2)/(35+2)=33/37
C1
sina+cosa=1/3
(sina+cosa)^2=1/9
sin^2+2sinacosa+cos^2=1/9
1+2sinacosa=1/9
2sinacosa=-8/9
sinacosa=-4/9
C2
5<span>√2сos(arctg(-1/7))
arctg(-1/7)=x
tgx=-1/7
1+tg^2(x)=1/cos^2(x)
1+1/49=1/cos^2(x)
50/49=1/cos^2(x)
cos^2(x)=49/50
cos(x)=7/5<span>√2
</span>5<span>√2*7/5<span>√2=7
</span></span>C3
√(-1-2cosx)
-1-2cosx<span>≥0
2cosx<span>≤-1
</span>cosx<span>≤-1/2
</span>arccos(-1/2)+2пk<span>≤x<span>≤2п-arccos(-1/2)+2пk
</span></span>2п/3+2пk<span>≤x<span>≤2п-2п/3+2пk
</span></span>2п/3+2пk<span>≤x<span>≤4п/3+2пk</span></span> </span></span>
Lgx=lg4+2lg(a-b)
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