Question

Tính giá trị biểu thức

Cosa=2/3. Tính A = (tan.a+3.cot.a)/(tan.a+cot.a)

Answer 1

Tính theo kiểu lớp 9 :)

\(cos\alpha=\frac{2}{3}\Rightarrow sin\alpha=\sqrt{1-cos^2\alpha}=\sqrt{1-\left(\frac{2}{3}\right)^2}=\frac{\sqrt{5}}{3}\Rightarrow\left\{{}\begin{matrix}tan\alpha=\frac{\frac{\sqrt{5}}{3}}{\frac{2}{3}}=\frac{\sqrt{5}}{2}\\cotg\alpha=\frac{\frac{2}{3}}{\frac{\sqrt{5}}{3}}=\frac{2\sqrt{5}}{5}\end{matrix}\right.\)

\(A=\frac{tan\alpha+3cotg\alpha}{tan\alpha+cotg\alpha}=\frac{\frac{\sqrt{5}}{2}+3.\frac{2\sqrt{5}}{5}}{\frac{\sqrt{5}}{2}+\frac{2\sqrt{5}}{5}}=\frac{17}{9}\)