Question

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Пожалуйста

Answer 1

1)Sin(α - β) +2SinβCosα = SinαCosβ - SinβCosα +2SinβCosα =

= SinαCosβ + SinβCosα = Sin(α + β) = Sinπ = 0

$2)a)Sin(\frac{\pi }{2}+\alpha)Cos(\pi-\alpha)=Cos\alpha*(-Cos\alpha)=-Cos^{2}\alpha$

$b)Ctg(\pi-\alpha)tg(\frac{3\pi }{2}-\alpha)=-Ctg\alpha*Ctg\alpha=-Ctg^{2}\alpha\\\\c)\frac{-Cos^{2}\alpha}{-Ctg^{2}\alpha}=\frac{Cos^{2}\alpha *Sin^{2}\alpha}{Cos^{2}\alpha}=Sin^{2}\alpha\\\\d)Cos^{2}\alpha+Sin^{2}\alpha=1$

Ответ :

$Cos^{2}\alpha+\frac{Sin(\frac{\pi }{2}+\alpha)Cos(\pi-\alpha)}{Ctg(\pi-\alpha)*tg(\frac{3\pi }{2}-\alpha)}=1$

3)Cos2005⁰Cos1960⁰ + Sin2005⁰Sin1960⁰ = Cos(2005⁰ - 1960⁰)=Cos45⁰ = √2/2