1) 11/30 + 17/36 = 66/180 + 85/180 = 151/180
2) 151/180 : 19/45 = 151/76 = 1 75/76
Ответ 1 75/76
1.
1)sin765=sin(720+45)=sin45=√2/2
2)cos19π/6=cos(3π+π/6)=cos(π+π/6)=-cosπ/6=-√3/2
2.
cosa=-√1-0,09=-√0,91=-0,1√91
3.
1)cosacosb+sinasinb-cosacosb+sinasinb=2sinasinb
2)(-sina-cosa)/(-2cosacosa+1)=-(sina+cosa)/(-2cos²a+sin²a+cos²a)=-(sina+cosa)/(sin²a-cos²a)=-(sina+cos)/(sina-cosa)(sina+cosa)=-1/(sina-cosa)=1/(cosa-sina)
4.sinxcos3x+cosxsin3x=-1
sin(x+3x)=-1
sin4x=-1
4x=-π/2+2πn
x=-π/8+πn/2
5.((sina/cosa+cosa/sina)*(cos²2a+sin²2a-cos²2a+sin²2a)= ((sin²a+cos²a)/sinacosa)*2sin²2a=2/sin2a*2sin²2a=4sin2a
Tg(a+b)=(tga+tgb)/(1-tgatgb);tg(a-b)=(tga-tgb)/(1+tgatgb)
-----------------------------
tg(a+π/4)+tg(a-π/4)=(tga+tgπ/4)/(1-tgatgπ/4)+(tga-tgπ/4)/(1+tgatgπ/4)=
=(tga+1)/(1-tga)+(tga-1)/(1+tga)=[(tga+1)²-(tga-1)²]/[(1-tga)(1+tga)]=
=(1+2tga+tg²a-tg²a+2tga-1)/(1-tg²a)=4tga/(1-tg²a)=2tg2a
4*(3*x+4)*(x+2)*(1-2*x)-3*(4*x+3)*(2-x)*(1+2*x) = -43*(2*x+3)*(x+2)-12
32 - 68*x^2 - 24*x - 24*x^3 - (3*(4*x + 3))*(2 - x)*(1 + 2*x) = -43*(2*x+3)*(x+2)-12
32 - 68*x^2 - 24*x - 24*x^3 - 18 - 51*x - 18*x^2 + 24*x^3 = -43*(2*x+3)*(x+2)-12
32 - 68*x^2 - 24*x - 24*x^3 - 18 - 51*x - 18*x^2 + 24*x^3 = - 258 - 301*x - 86*x^2 - 12
<span>284 + 226*x = 0
</span>226x=-284
x= - 284/226 <span> | :2
</span>x= - 142/113
+{4x-5y=83
+{2x+5y=29
6x=112|:6
x=18 2/3
2*56/3-5y=83
-5y=83-112/3
-5y=83-37 1/3
-5y=45 2/3|:(-5)
y=137/3*(-1/5)=-137/15=-9 2/15