Cho hai góc nhọn a và b với \(\sin a = \frac{1}{3}, \sin b = \frac{1}{2}\).

* Hướng dẫn giải

Ta có \(\left\{ \begin{array}{l}
0 < a < \frac{\pi }{2}\\
\sin a = \frac{1}{3}
\end{array} \right. \Rightarrow \cos a = \frac{{2\sqrt 2 }}{3}\); \(\left\{ \begin{array}{l}
0 < b < \frac{\pi }{2}\\
\sin b = \frac{1}{2}
\end{array} \right. \Rightarrow \cos b = \frac{{\sqrt 3 }}{2}\)

\(\sin 2\left( {a + b} \right) = 2\sin \left( {a + b} \right).\cos \left( {a + b} \right) = 2\left( {\sin a.\cos b + \sin b.\cos a} \right)\left( {\cos a.\cos b + \sin a.\sin b} \right) = \frac{{4\sqrt 2  + 7\sqrt 3 }}{{18}}\)