Đề bài

Không dùng máy tính cầm tay, tính: a) \(\cos \frac{{3\pi }}{8}\cos \frac{\pi }{8} - \sin \frac{{3\pi }}{8}\sin \frac{\pi }{8};\) b) \(\sin {15^0}\sin {75^0};\) c) \(\cos \left( { - {{15}^0}} \right) + \cos {255^0};\) d) \(\frac{{\cos \frac{{2\pi }}{9} - \cos \frac{{4\pi }}{9}}}{{\sin \frac{{2\pi }}{9} - \sin \frac{{4\pi }}{9}}}.\)

Lời giải chi tiết

a) \(\cos \frac{{3\pi }}{8}\cos \frac{\pi }{8} - \sin \frac{{3\pi }}{8}\sin \frac{\pi }{8} = \cos \left( {\frac{{3\pi }}{8} + \frac{\pi }{8}} \right) = \cos \frac{\pi }{2} = 0\)b) \(\sin {15^0}\sin {75^0} = \frac{1}{2}\left[ {\cos \left( { - {{60}^0}} \right) - \cos {{90}^0}} \right] = \frac{1}{4}\)c) \(\cos \left( { - {{15}^0}} \right) + \cos {255^0} = 2\cos {120^0}\cos \left( { - {{135}^0}} \right) = \frac{{\sqrt 2 }}{2}\)d) \(\frac{{\cos \frac{{2\pi }}{9} - \cos \frac{{4\pi }}{9}}}{{\sin \frac{{2\pi }}{9} - \sin \frac{{4\pi }}{9}}}. = \frac{{ - 2\sin \frac{\pi }{3}\sin \left( { - \frac{\pi }{9}} \right)}}{{2\cos \frac{\pi }{3}\sin \left( { - \frac{\pi }{9}} \right)}} = \frac{{ - \sin \frac{\pi }{3}}}{{\cos \frac{\pi }{3}}} =  - \sqrt 3 \)