oblicz

[bullay]

Oblicz:
\(\displaystyle{ cos^2\beta + cos^2(\alpha-\beta)-2cos\beta* cos\alpha*cos(\alpha-\beta)}\)

[Lady Tilly]

\(\displaystyle{ sin^{2}\beta+(cos\alpha{\cdot}cos\beta+sin\alpha{\cdot}sin\beta)^{2}-2cos\alpha{\cdot}cos\beta(cos\alpha{\cdot}cos\beta+sin\alpha{\cdot}sin\beta)=cos^{2}\beta-cos^{2}\alpha{\cdot}cos^{2}\beta+sin^{2}\alpha{\cdot}sin^{2}\beta=1-cos^{2}\alpha=sin^{2}\alpha}\)