<span>a) sin 13п/6 =sin(12</span>π/6+π/6)=sin(2π+π/6)=sin π/6=1/2=0.5
<span>б) tg (-11п/6) =-tg(11</span>π/6)=-tg(12π/6-π/6)=-tg(2π-π/6)=tgπ/6=√3/3
<span>в)cos п + ctg 4п/3 =-1+</span>√3/3
<span>г)tg п/4 ctg (-п/4) + cos 3п/2 sin п/2 =-tg </span>π/4*ctg π/4+0*1=-√2/2*√2/2+0=-2/4=-1/2=-0.5
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д) sin 405º + cos 225º tg 225º=sin(360+45)+cos(180+45)*tg(180+45)=sin45+(-cos45)*tg45=</span>√2/2-√2/2*1=0
<span>sin(a +b) +sin(-a) * cos(-b)=sina cosb+cosasinb-sina cosb=cosa *sinb</span>
-8; -6,5; -5;...
a1=-8; a2=-6,5; d=-6,5-(-8)=-6,5+8=1,5.
a10=a1+9d=-8+9*1,5=-8+13,5=5,5.
S(10)=(a1+a10)*10/2=(-8+5,5)*5=-2,5*5=-12,5.
Ответ: -12,5.
x/(x+8) + (x+8)/(x-8) = (x² + x + 72)/(x² - 64)
x/(x+8) + (x+8)/(x-8) = (x² + x + 72)/((x - 8)(x + 8))|·(x - 8)(x + 8)
ОДЗ: x ≠ -8; x≠8
x(x-8) + (x+8)² = x² + x + 72;
x² - 8x + x² + 64 + 16x - x² - x - 72 = 0;
x² + 7x - 8 = 0;
x₁ = 1; x₂ = -8 - не задовольняє ОДЗ
Відповідь: 1.