"prosta" tożsamość

[snajper0208]

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

[Azai]

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