Подробное решение обязательно! sin(arctg(8/15)-arcsin(8/17))

[latex]sin(x-y)=sinx*cosy-siny*cosx[/latex] [latex]sin(arctg \frac{8}{15}-arcsin \frac{8}{17})=sin(arctg \frac{8}{15})*cos(arcsin \frac{8}{17})-sin(arcsin \frac{8}{17})*cos(arctg \frac{8}{15})[/latex] a, b - катеты прямоугольного треугольника c - гипотенуза [latex]tg \alpha = \frac{b}{a} [/latex] [latex]sin \alpha = \frac{b}{c} [/latex] [latex]cos \alpha = \frac{a}{c} [/latex] [latex]c= \sqrt{a^{2}+b^{2}} [/latex] [latex]a= \sqrt{c^{2}-b^{2}} [/latex] [latex]sin(arctgx)= \frac{b}{\sqrt{a^{2}+b^{2}}} [/latex] [latex]cos(arctgx)= \frac{a}{\sqrt{a^{2}+b^{2}}}[/latex] [latex]sin(arcsinx)=x[/latex] [latex]cos(arcsinx)= \frac{ \sqrt{c^{2}-b^{2}}}{c}[/latex], где [latex]x= \frac{b}{a}[/latex] a=15, b=8, c=17 [latex]sin(arctg \frac{8}{15})= \frac{8}{17} [/latex], где [latex]cos(arctg \frac{8}{15})= \frac{15}{17}[/latex] b=8, c=17, a=15 [latex]sin(arcsin \frac{8}{15})= \frac{8}{15}[/latex] [latex]cos(arcsin \frac{8}{17})= \frac{15}{17}[/latex] [latex]\frac{8}{17}*\frac{15}{17}-\frac{8}{17}*\frac{15}{17}=0[/latex]