1)Sin(α - β) +2SinβCosα = SinαCosβ - SinβCosα +2SinβCosα =
= SinαCosβ + SinβCosα = Sin(α + β) = Sinπ = 0
![2)a)Sin(\frac{\pi }{2}+\alpha)Cos(\pi-\alpha)=Cos\alpha*(-Cos\alpha)=-Cos^{2}\alpha](https://tex.z-dn.net/?f=2%29a%29Sin%28%5Cfrac%7B%5Cpi+%7D%7B2%7D%2B%5Calpha%29Cos%28%5Cpi-%5Calpha%29%3DCos%5Calpha%2A%28-Cos%5Calpha%29%3D-Cos%5E%7B2%7D%5Calpha)
![b)Ctg(\pi-\alpha)tg(\frac{3\pi }{2}-\alpha)=-Ctg\alpha*Ctg\alpha=-Ctg^{2}\alpha\\\\c)\frac{-Cos^{2}\alpha}{-Ctg^{2}\alpha}=\frac{Cos^{2}\alpha *Sin^{2}\alpha}{Cos^{2}\alpha}=Sin^{2}\alpha\\\\d)Cos^{2}\alpha+Sin^{2}\alpha=1](https://tex.z-dn.net/?f=b%29Ctg%28%5Cpi-%5Calpha%29tg%28%5Cfrac%7B3%5Cpi+%7D%7B2%7D-%5Calpha%29%3D-Ctg%5Calpha%2ACtg%5Calpha%3D-Ctg%5E%7B2%7D%5Calpha%5C%5C%5C%5Cc%29%5Cfrac%7B-Cos%5E%7B2%7D%5Calpha%7D%7B-Ctg%5E%7B2%7D%5Calpha%7D%3D%5Cfrac%7BCos%5E%7B2%7D%5Calpha+%2ASin%5E%7B2%7D%5Calpha%7D%7BCos%5E%7B2%7D%5Calpha%7D%3DSin%5E%7B2%7D%5Calpha%5C%5C%5C%5Cd%29Cos%5E%7B2%7D%5Calpha%2BSin%5E%7B2%7D%5Calpha%3D1)
Ответ :
![Cos^{2}\alpha+\frac{Sin(\frac{\pi }{2}+\alpha)Cos(\pi-\alpha)}{Ctg(\pi-\alpha)*tg(\frac{3\pi }{2}-\alpha)}=1](https://tex.z-dn.net/?f=Cos%5E%7B2%7D%5Calpha%2B%5Cfrac%7BSin%28%5Cfrac%7B%5Cpi+%7D%7B2%7D%2B%5Calpha%29Cos%28%5Cpi-%5Calpha%29%7D%7BCtg%28%5Cpi-%5Calpha%29%2Atg%28%5Cfrac%7B3%5Cpi+%7D%7B2%7D-%5Calpha%29%7D%3D1)
3)Cos2005⁰Cos1960⁰ + Sin2005⁰Sin1960⁰ = Cos(2005⁰ - 1960⁰)=Cos45⁰ = √2/2
H - высота треугольника
а - основание треугольника
h - высота прямоугольника
b - основание прямоугольника
b=a*(1-h/H)
S=b*h=a*(1-h/H)*h
dS/dh = a*(1-h/H)-ah/H=a*(1-2h/H)
dS/dh = 0 при 1-2h/H=0 при h=H/2
S мах = a*(1-h/H)*h = a*(1-(H/2)/H)*H/2 = a*H*(1-1/2)*1/2 = a*H*1/4 = 12*10*1/4=30
ответ 30 см^2