Question

[Dark Knight Rises]

Tính :

Sin α  * Cos α ​biết tg α + cotg α = 3

​(Sin α - ​Cos α)^2 - 2Sin​ α*Cos ​α - 1​

Answer 1

[Trần Phúc]

\(\tan\alpha+\cot\alpha=3\)

\(\Leftrightarrow\frac{\sin\alpha}{\cos\alpha}+\frac{\cos\alpha}{\sin\alpha}=3\)

\(\Leftrightarrow\frac{\sin^2\alpha+\cos^2\alpha}{\sin\alpha.\cos\alpha}=3\)

\(\Leftrightarrow\frac{1}{\sin\alpha.\cos\alpha}=3\)

\(\Rightarrow\sin\alpha.\cos\alpha=\frac{1}{3}\)