Question

Помогите с решение пожалуйста

Answer 1

$1); ; cos(-45^circ )=cos45^circ =frac{sqrt2}{2}\\sin405^circ =sin(360^circ+45^circ )=sin45^circ =frac{sqrt2}{2}\\cos900^circ =cos(720^circ +180^circ )=cos180^circ =-1\\tg(-frac{pi}{3})=-tgfrac{pi}{3}=-sqrt3\\ctg(-frac{7pi }{3})=-ctg(2pi +frac{pi}{3})=-ctgfrac{pi}{3}=-frac{sqrt3}{3}\\frac{cos(-45^circ )cdot sin405^circ -cos900^circ }{tg(-frac{pi}{3})cdot ctg(-frac{7pi}{3})}=frac{frac{sqrt2}{2}cdot frac{sqrt2}{2}+1}{sqrt3cdot frac{sqrt3}{3}}=frac{frac{1}{2}+1}{1}=1,5$

$2); ; 1-sinfrac{pi}{6}+sin^2frac{pi}{6}-sin^3frac{pi}{6}+,,,=1-frac{1}{2}+(frac{1}{2})^2-(frac{1}{2})^3+...=\\=Big (underbrace {1+(frac{1}{2})^2+(frac{1}{2})^4+...}_{b_1=1; ,; q=frac{1}{4}}Big )-Big (, underbrace {frac{1}{2}+(frac{1}{2})^3+(frac{1}{2})^5+...}_{b_1=1/2; ,; q=frac{1}{4}}Big )=\\=frac{1}{1-(frac{1}{2})^2}-frac{frac{1}{2}}{1-(frac{1}{2})^2}=frac{1-frac{1}{2}}{1-frac{1}{4}}=frac{frac{1}{2}}{frac{3}{4}}=frac{2}{3}$