Đề bài
Cho \(\cos \alpha = \dfrac{3}{4},\sin \alpha > 0;\sin \beta = \dfrac{3}{5},\cos \beta < 0\).
Hãy tính \(\cos 2\alpha ,\sin 2\alpha ,\cos 2\beta ,\sin 2\beta ,\) \(\cos \left( {\alpha + \beta } \right),\sin \left( {\alpha - \beta } \right)\)
Lời giải chi tiết
\(\cos 2\alpha = \dfrac{1}{8};\sin 2\alpha = \dfrac{{3\sqrt 7 }}{8};\)
\(\cos 2\beta = \dfrac{7}{{25}};\sin 2\beta = - \dfrac{{24}}{{25}}.\)
\(\cos \left( {\alpha + \beta } \right) = - \dfrac{3}{5}\left( {1 + \dfrac{{\sqrt 7 }}{4}} \right);\)
\(\sin \left( {\alpha - \beta } \right) = - \dfrac{1}{5}\left( {\sqrt 7 + \dfrac{9}{4}} \right).\)
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