[tex]a=\sqrt{2+\sqrt2}[/tex]
[tex]c=2[/tex]
Obliczam b
[tex]a^2+b^2=c^2[/tex]
[tex](\sqrt{2+\sqrt2})^2+b^2=2^2[/tex]
[tex]2+\sqrt2+b^2=4[/tex]
[tex]b^2=4-2-\sqrt2[/tex]
[tex]b^2=2-\sqrt2[/tex]
[tex]b=\sqrt{2-\sqrt2}[/tex]
Obliczam tgα
[tex]tg\alpha=\frac{b}{a}[/tex]
[tex]tg\alpha=\frac{\sqrt{2-\sqrt2}}{\sqrt{2+\sqrt2}}[/tex]
[tex]tg\alpha=\frac{\sqrt{2-\sqrt2}}{\sqrt{2+\sqrt2}}\cdot\frac{\sqrt{2-\sqrt2}}{\sqrt{2-\sqrt2}}[/tex]
[tex]tg\alpha=\frac{2-\sqrt2}{\sqrt{(2+\sqrt2)(2-\sqrt2)}}[/tex]
[tex]tg\alpha=\frac{2-\sqrt2}{\sqrt{4-2}}[/tex]
[tex]tg\alpha=\frac{2-\sqrt2}{\sqrt{2}}[/tex]
[tex]tg\alpha=\frac{2\sqrt2-2}{2}[/tex]
[tex]tg\alpha=\sqrt2-1[/tex]
