[latex]sin^{2}alpha + cos^{2}alpha = 1[/latex] [latex]sin^{2}alpha + cos^{2}alpha = 1 [/latex] [latex]sin^{2}alpha = 1 - (frac{15}{17})^{2} [/latex] [latex]sin^{2}alpha = frac{64}{289} [/latex] [latex]sinalpha = frac{8}{17}[/latex] [latex] frac{4cos alpha -tg alpha }{sin alpha +tg alpha } = frac{4cos alpha - frac{sinj alpha }{cos alpha } }{sinalpha+frac{sin alpha}{cosalpha} } = frac{4*frac{15}{17}-frac{8}{15}}{frac{8}{17}+frac{8}{15}}=frac{frac{764}{255}}{frac{256}{255}}=frac{191}{64}[/latex]
[latex]sin^2alpha+cos^2alpha=1\\sin^2alpha+(frac{15}{17})^2=1\\sin^2alpha+frac{225}{289}=1\\sin^2alpha=1-frac{225}{289}\\sin^2alpha=frac{64}{289}\\sinalpha=sqrtfrac{64}{289}\\sinalpha=frac{8}{17}\-----------------------[/latex] [latex]tgalpha=frac{sinalpha}{cosalpha}\\tgalpha=frac{8}{17}:frac{15}{17}=frac{8}{17}cdotfrac{17}{15}=frac{8}{15}\\----------------------------\\frac{4cosalpha-tgalpha}{sinalpha+tgalpha}=(4cdotfrac{15}{17}-frac{8}{15}):(frac{8}{17}+frac{8}{15})=(frac{60}{17}-frac{8}{15}):(frac{8}{17}+frac{8}{15})\\=frac{60cdot15-8cdot17}{17cdot15}:frac{8cdot15+8cdot17}{17cdot15}=frac{900-136}{17cdot15}cdotfrac{17cdot15}{120+136}=frac{764}{256}=frac{191}{64}=2frac{63}{64}[/latex]
