Question

ФАСТОМ!!! Допоможіть с аглеброю

Answer 1

$\displaystyle\bf\\a)\\\\Cos\frac{\pi }{18} Cos\frac{4\pi }{9} -Sin\frac{\pi }{18} Sin\frac{4\pi }{9} =Cos\Big(\frac{\pi }{18} +\frac{4\pi }{9} \Big)=\\\\\\=Cos\frac{\pi +8\pi }{18} =Cos\frac{9\pi }{18} =Cos\frac{\pi }{2} =0\\\\b)$

$\displaystyle\bf\\\frac{Ctg\dfrac{7\pi }{16} \cdot Ctg\dfrac{3\pi }{16} }{Ctg\dfrac{7\pi }{16}+Ctg\dfrac{3\pi }{16} } =Ctg\Big(\frac{7\pi }{16} +\frac{3\pi }{16} \Big)=Ctg\frac{10\pi }{16} =Ctg\frac{5\pi }{8}=\\\\\\=Ctg\Big(\frac{\pi }{2} +\frac{\pi }{8} \Big)=-tg\frac{\pi }{8}$