ГДЗ по алгебре и начала математического анализа 10 класс Колягин Задание 1008

\[\boxed{\mathbf{1008.}}\]

\[\left( \text{asin}\beta + b\cos\beta \right)^{2} +\]

\[+ \left( b\sin\beta - a\cos\beta \right)^{2} =\]

\[= a^{2}\sin^{2}\beta + 2ab \cdot \sin\beta\cos\beta +\]

\[+ b^{2}\cos^{2}\beta + b^{2}\sin^{2}\beta -\]

\[- 2ab \cdot \sin\beta\cos\beta + a^{2}\cos^{2}\beta =\]

\[= a^{2}\left( \sin^{2}\beta + \cos^{2}\beta \right) +\]

\[+ b^{2}\left( \cos^{2}\beta + \sin^{2}\beta \right) = a^{2} + b^{2}.\]