oblicz wartosć wyrazenia 3sin[latex] alpha [/latex] + cos[latex] alpha [/latex] dielone przez cos[latex] alpha [/latex] - 3sin[latex] alpha [/latex] jeśli [latex]tg alpha = 2[/latex] i [latex] alpha [/latex] jest kątem ostrym

[latex]tg alpha = 2\tg alpha = frac{sin alpha }{cos alpha } = 2\sin alpha =2cos alpha \\frac{3sin alpha+cos alpha }{cos alpha -3sin alpha } = frac{3(2cos alpha) +cos alpha }{cos alpha -3(2cos alpha )} = \frac{6cos alpha +cos alpha }{cos alpha-6cos alpha }= frac{7cos alpha }{-5cos alpha } = -frac{7}{5} = -1frac{2}{5}[/latex]