Hãy tính \[\cos 2\alpha ,\sin 2\alpha ,\cos 2\beta ,\sin 2\beta ,\] \[\cos \left[ {\alpha + \beta } \right],\sin \left[ {\alpha - \beta } \right]\]
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
\[\cos 2\alpha = \dfrac{1}{8};\sin 2\alpha = \dfrac{{3\sqrt 7 }}{8};\]
\[\cos 2\beta = \dfrac{7}{{25}};\sin 2\beta = - \dfrac{{24}}{{25}}.\]
\[\cos \left[ {\alpha + \beta } \right] = - \dfrac{3}{5}\left[ {1 + \dfrac{{\sqrt 7 }}{4}} \right];\]
\[\sin \left[ {\alpha - \beta } \right] = - \dfrac{1}{5}\left[ {\sqrt 7 + \dfrac{9}{4}} \right].\]