Ну помогиииитеее 1-tg^2 π/8

Решите задачу:

$1-tg^2a=1- \frac{sin^2a}{cos^2a}= \frac{cos^2a-sin^2a}{cos^2a} = \frac{cos2a}{\frac{1+cos2a}{2}} = \frac{2cos2a}{1+cos2a} \\\\Forvylu:\; \; cos^2a-sin^2a=cos2a,\; \; cos^2a=\frac{1+cos2a}{2}\\\\1-tg^2\frac{\pi}{8}=\frac{2cos\frac{\pi}{4}}{1+cos\frac{\pi}{4}}= \frac{2\cdot \frac{\sqrt2}{2}}{1+\frac{\sqrt2}{2}} =\frac{2\sqrt2}{2+\sqrt2}= \frac{2\sqrt2(2-\sqrt2)}{4-2} =\sqrt2(2-\sqrt2)\\$