Если tg(a/2) = √2, то cos2a = ?...

[latex]tg\frac{a}{2}=\sqrt2\; ,\; \; cos2a=?\\\\Formylu:\; \; \; cos2a=2cos^2a-1\; ;\; \; \; cosa=\frac{1-tg^2\frac{a}{2}}{1+tg^2\frac{a}{2}}\; ;\\\\cosa=\frac{1-(\sqrt2)^2}{1+(\sqrt2)^2}=\frac{1-2}{1+2}=-\frac{1}{3}cos2a=2\cdot (-\frac{1}{3})^2-1=\frac{2}{9}-1=-\frac{7}{9}[/latex]