Biểu thức cos(-23pi/6) - 1/cos^2 16pi/3 + cot 23pi/6 = ? căn 3/2 - 5

* Hướng dẫn giải

Đáp án D

$$\begin{gathered} \cos \left(-\frac{23\pi }{6}\right)-\frac{1}{{\cos }^2\frac{16\pi }{3}}+\cot \frac{23\pi }{6} \\ =\cos \left(-4\pi +\frac{\pi }{6}\right)-\frac{1}{\frac{1+\cos \frac{32\pi }{3}}{2}}+\cot \left(4\pi -\frac{\pi }{6}\right) \\ =\cos \frac{\pi }{6}-\frac{2}{1+\cos \left(10\pi +\frac{2\pi }{3}\right)}+\cot \left(-\frac{\pi }{6}\right) \\ =\cos \frac{\pi }{6}-\frac{2}{1+\cos \frac{2\pi }{3}}-\cot \frac{\pi }{6} \\ =\frac{\sqrt{3}}{2}-\frac{2}{1-\frac{1}{2}}-\sqrt{3}=-\frac{\sqrt{3}}{2}-4 \end{gathered}$$