Tính giá trị ​\( C = {(3\sin \alpha + 4\cos \alpha )^2} + {\left( {4\sin \alpha - 3\cos \alpha } \right)^2}\)

* Hướng dẫn giải

Ta có 

\(\begin{array}{l} C = {(3\sin \alpha + 4\cos \alpha )^2} + {\left( {4\sin \alpha - 3\cos \alpha } \right)^2} = 9{\sin ^2}\alpha + 24\sin \alpha .\cos \alpha + 16{\cos ^2}\alpha + 16{\sin ^2}\alpha - 24\sin \alpha \cos \alpha + 9{\cos ^2}\alpha \\ = 25{\sin ^2}\alpha + 25{\cos ^2}\alpha = 25\left( {{{\sin }^2}\alpha + {{\cos }^2}\alpha } \right) = 25.1 = 25 \end{array}\)