Question

[Nguyễn Phương Linh]

Giúp mình câu này nhé mọi người <3 Kamsamita

Answer 1

[Lê Thị Thục Hiền]

Vì \(\pi< \alpha< \dfrac{3\pi}{2}\) \(\Rightarrow\dfrac{\pi}{2}< \dfrac{\alpha}{2}< \dfrac{3\pi}{4}\)

\(\Rightarrow sin\dfrac{\alpha}{2}>0;cos\dfrac{\alpha}{2}< 0\)

\(\pi< \alpha< \dfrac{3\pi}{2}\Rightarrow cos\alpha< 0\)

\(\Rightarrow cos\alpha=-\sqrt{1-sin^2\alpha}=-\dfrac{3}{5}\)

Có \(sin^2\dfrac{\alpha}{2}=\dfrac{1-cosa}{2}=\dfrac{4}{5}\Rightarrow sin\dfrac{\alpha}{2}=\sqrt{\dfrac{4}{5}}=\dfrac{2\sqrt{5}}{5}\)

\(cos^2\dfrac{\alpha}{2}=\dfrac{1+cosa}{2}=\dfrac{1}{5}\Rightarrow cos\dfrac{\alpha}{2}=-\sqrt{\dfrac{1}{5}}=-\dfrac{\sqrt{5}}{5}\)

\(tan\dfrac{\alpha}{2}=\dfrac{sin\dfrac{\alpha}{2}}{cos\dfrac{\alpha}{2}}=-2\)

\(cot\dfrac{\alpha}{2}=-\dfrac{1}{2}\)