<span><span><span>Применим формулу замены произведения косинусов их суммой
cos α · cos β</span>
=
(cos(α-β) + cos(α+β))/
</span><span>
2</span></span>
cos44*cos16=1/2(cos60+cos28)=1/2(1/2+cos28), cos60=1/2
cos 59*cos31=1/2(cos90+cos28)=1/2<span>cos28, </span> cos90=0
1/2(1/2+cos28)-1/2<span>cos28=1/4+1/2</span>cos28-1/2cos28=1/4
......,,,,,,,......,,,,,,,
А1
а)Sin11π/3 = Sin(4π - π/3) =- Sin π/3 = - √3/2
б)Cos(-4π/3) = Cos4π/3 = Сos(π + π/3) = -Cosπ/3 = -1/2
в)tg 13π/4 = tg(3π + π/4) = tgπ/4 = 1
г) Sin 29π/3 = Sin(10π - π/3) = Sinπ/3 = √3/2
д)Ctg (-2π/30 = -Ctg2π/3 = -Ctg(π - π/3) = Ctg π/3 = 1/√3
В1
-Cost·tg t + Sint + tgt = -Sin t + Sin t + tg t = tg t
1) 1000 - 30 = 970 (насосов ) исправны
2) 970 : 1000 = 0,97
Ответ: вероятность исправности выбранного насоса = 0,97