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[tex]\alpha\in(0^o;90^o)\\\\sin\alpha=\frac{1}{4}\\\\sin^2\alpha+cos^2\alpha=1\\\\(\frac{1}{4})^2+cos^2\alpha=1\\\\\frac{1}{16}+cos^2\alpha=1 \ \ /-\frac{1}{16}\\\\cos^2\alpha=\frac{15}{16}\\\\cos\alpha=\frac{\sqrt{15}}{\sqrt{16}}=\frac{\sqrt{15}}{4}\\\\tg\alpha=sin\alpha:cos\alpha=\frac{1}{4}:\frac{\sqrt{15}}{4}=\frac{1}{4}\cdot\frac{4}{\sqrt{15}}=\frac{1}{\sqrt{15}}=\frac{\sqrt{15}}{15}\\\\-3+4tg^2\alpha=-3+4\cdot(\frac{\sqrt{15}}{15})^2=-3+4\cdot\frac{15}{225}=-3+4\cdot\frac{1}{15}=-3+\frac{4}{15}[/tex]
[tex]\huge\boxed{-3+4tg^2\alpha=-2\frac{11}{15}}\\[/tex]
