Bài 1.13 trang 19

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) $\frac{\cos \frac{2\pi }{9}-\cos \frac{4\pi }{9}}{\sin \frac{2\pi }{9}-\sin \frac{4\pi }{9}}.=\frac{-2\sin \frac{\pi }{3}\sin \left(-\frac{\pi }{9}\right)}{2\cos \frac{\pi }{3}\sin \left(-\frac{\pi }{9}\right)}=\frac{-\sin \frac{\pi }{3}}{\cos \frac{\pi }{3}}=-\sqrt{3}$