Question

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Answer 1

Ответ:

-sin(2a)

Объяснение:

а)cos(t)cos(s) - sin(t)sin(s) = cos(t+s)

sin(t-s) = -sin(2a)

б)Через упрощение добиваемся:

cos(t)cos(s) - sin(t)sin(s) = cos(t+s)

cos(Pi/2 + 2a) = -sin(t)

-sin(2a)

Answer 2

$\displaystyle\bf\\1)\\\\Sin3\alpha Cos5\alpha -Sin5\alpha Cos3\alpha =Sin\Big(3\alpha -5\alpha \Big)=Sin\Big(-2\alpha \Big)=-Sin2\alpha \\\\\\2)\\\\Cos\Big(\frac{\pi }{10} +\alpha \Big) Cos\Big(\frac{2\pi }{5} +\alpha \Big)-Sin\Big(\frac{\pi }{10} +\alpha \Big) Sin\Big(\frac{2\pi }{5} +\alpha \Big)=\\\\\\=Cos\Big(\frac{\pi }{10} +\alpha +\frac{2\pi }{5} +\alpha \Big)=Cos\Big(\frac{5\pi }{10} +2\alpha \Big)=Cos\Big(\frac{\pi }{2}+2\alpha \Big)=-Sin2\alpha$