Question

Помогите с алгеброй пожалуйста

1) $(1,2 \sqrt[3]{100\sqrt{10} } + 8,8 \sqrt{10\sqrt[3]{100} } )^{ \frac{-11}{12} }$

2) $4sin( \frac{\pi }{2} + \alpha )-sin( \pi + \alpha )*cos \alpha$ , при $\alpha = \frac{\pi}{24}$

Answer 1

$(1,2\sqrt[3]{100\sqrt{10}}+8,8\sqrt{10\sqrt[3]{100}})^{-\frac{11}{12}}=\\\\=(1,2\sqrt[3]{\sqrt{100000}}}+8,8\sqrt{\sqrt[3]{100000}})^{-\frac{11}{12}}=\\\\=(1,2\sqrt[6]{100000}+8,8\sqrt[6]{100000})^{-\frac{11}{12}}=\\\\=(10\sqrt[6]{100000})^{-\frac{11}{12}}=(10^{1+\frac{5}{6}})^{-\frac{11}{12}}=10^{\frac{11}{6}-\frac{11}{12}}=10^{\frac{11}{12}}\\\\\\4sin(\frac{\pi}{2}+ \alpha )-sin(\pi + \alpha )\cdot cos \alpha =4cos \alpha +sin \alpha \cdot cos \alpha =\\\\=cos \alpha \cdot (4+sin \alpha )=$

$=cos\frac{\pi}{24}(4+sin\frac{\pi}{24})$