Cho \(\sin a=\frac{3}{5}, \cos a0\). Hãy tính \(\sin \left( a-b \right)\)?

* Hướng dẫn giải

Ta có

. \(\left\{ \begin{array}{l} \sin a = \frac{3}{5}\\ \cos a < 0 \end{array} \right.\,\,\, \Rightarrow \cos a = - \sqrt {1 - {{\sin }^2}a} = - \frac{4}{5}\)
. \(\left\{ \begin{array}{l} \cos b = \frac{3}{4}\\ \sin b > 0 \end{array} \right.\,\,\, \Rightarrow \sin b = \sqrt {1 - {{\cos }^2}b} = \frac{{\sqrt 7 }}{4}\)

Vậy \(\sin \left( {a - b} \right) = \sin a\cos b - \cos a\sin b = \frac{3}{5}.\frac{3}{4} - \left( { - \frac{4}{5}} \right).\frac{{\sqrt 7 }}{4} = \frac{1}{5}\left( {\sqrt 7 + \frac{9}{4}} \right)\).