Question

Cho sinα = \(\dfrac{3}{5}\) ; 90độ < α < 180độ

Tính A = \(\dfrac{3sin\alpha+cos\alpha}{tan\alpha-cot\alpha}\) 

Các bạn ơi giải giúp mình với ạ 

Answer 1

\(sin\alpha=sin\left(180-\alpha\right)=\dfrac{3}{5}\Rightarrow cos\left(180-a\right)=\sqrt{1-sin^2\alpha}=\dfrac{4}{5}\Rightarrow cos\alpha=-\dfrac{4}{5}\)

\(\Rightarrow tan\alpha=\dfrac{sin\alpha}{cos\alpha}=\dfrac{\dfrac{3}{5}}{-\dfrac{4}{5}}=-\dfrac{3}{4}\Rightarrow cot\alpha=-\dfrac{4}{3}\)

\(\Rightarrow A=\dfrac{3.\dfrac{3}{5}-\dfrac{4}{5}}{-\dfrac{3}{4}+\dfrac{4}{3}}=\dfrac{12}{7}\)