Niech
BC=a
AC=b
\frac{a}{b}=\sqrt2
\frac{a}{sin\alpha}=\frac{b}{sin\beta}
b*sin\alph=a*sin\beta /:sin\beta
\frac{bsin\alpha}{sin\beta}=a/:b
\frac{sin\alpha}{sin\beta}=\frac{a}{b}=\sqrt2
\frac{sin\alpha}{sin\beta}=\sqrt2/^2
\frac{sin^2\alpha}{sin^2\beta}=2/*sin^2\beta
1-cos^2\alpha=2(1-cos\beta)
1-cos^2\alpha=2-2cos\beta
-cos^2\alpha=2-1-2cos^2\beta
-cos^2\alpha=1-2cos\beta/*(-1)
cos^2\alpha=2cos^2\beta-1