Cho biết cot alpha = 5. Tính giá trị của E = 2cos^2 alpha + 5sin alpha.cos alpha + 1

* Hướng dẫn giải

Đáp án D

Ta có:

$$\begin{gathered} E=2{\cos }^2\alpha +5\sin \alpha \cos \alpha +1 \\ ={\sin }^2\alpha \left(2.\frac{{\cos }^2\alpha }{{\sin }^2\alpha }+5\frac{\cos \alpha }{\sin \alpha }+\frac{1}{{\sin }^2\alpha }\right) \\ =\left(\frac{1}{{\cot }^2\alpha +1}\right)\left(2.{\cot }^2\alpha +5\cot \alpha +\frac{1}{\frac{1}{{\cot }^2\alpha +1}}\right) \\ =\left(\frac{1}{{\cot }^2\alpha +1}\right)\left(2.{\cot }^2\alpha +5\cot \alpha +{\cot }^2\alpha +1\right) \\ =\left(\frac{1}{{\cot }^2\alpha +1}\right)\left(3{\cot }^2\alpha +5\cot \alpha +1\right) \\ =\frac{1}{5^2+1}\left({3.5}^2+5.5+1\right)=\frac{101}{26} \end{gathered}$$