Найти tgα, если tg(α-π/4) = 3/4

  [latex]tg\frac{\pi}{4}=1\\tg(\alpha-\beta)=\frac{tg\alpha-tg\beta}{1+tg\alpha*tg\beta}\\\\\\tg(\alpha-\frac{\pi}{4})=\frac{tg\alpha-tg\frac{\pi}{4}}{1+tg\alpha*tg\frac{\pi}{4}}\\\frac{3}{4}=\frac{tg\alpha-1}{1+tg\alpha}\\3(1+tg\alpha)=4(tg\alpha-1)\\3-3tg\alpha=4tg\alpha-4\\7tg\alpha=7\\tg\alpha=1[/latex]