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

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

\(\Rightarrow\) tan \(\alpha\) = \(\dfrac{sin\alpha}{cos\alpha}=\dfrac{-\sqrt{2}}{4}\)

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

Chúc bn học tốt!

$\sin \alpha =2$?? $\sin \alpha \in [-1;1]$ với mọi $\alpha$ mà bạn. Bạn xem lại đề.

a: \(\cos\alpha=\dfrac{1}{2}\)

\(\tan\alpha=\sqrt{3}\)

\(\cot\alpha=\dfrac{\sqrt{3}}{3}\)

Chọn C.

Ta có tan α – cotα = 1 

Do  suy ra tanα < 0 nên 

Thay

 và

vào P  ta được 

Cho α là góc nhọn, sinα = 1/2. Tính cosα; tanα; cotα

Ta có: sin 2 α + cos 2 α = 1

a: pi/2<a<pi

=>sin a>0

\(sina=\sqrt{1-\left(-\dfrac{1}{\sqrt{3}}\right)^2}=\dfrac{\sqrt{2}}{\sqrt{3}}\)

\(sin\left(a+\dfrac{pi}{6}\right)=sina\cdot cos\left(\dfrac{pi}{6}\right)+sin\left(\dfrac{pi}{6}\right)\cdot cosa\)

\(=\dfrac{\sqrt{3}}{2}\cdot\dfrac{\sqrt{2}}{\sqrt{3}}+\dfrac{1}{2}\cdot-\dfrac{1}{\sqrt{3}}=\dfrac{\sqrt{6}-2}{2\sqrt{3}}\)

b: \(cos\left(a+\dfrac{pi}{6}\right)=cosa\cdot cos\left(\dfrac{pi}{6}\right)-sina\cdot sin\left(\dfrac{pi}{6}\right)\)

\(=\dfrac{-1}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{2}-\dfrac{\sqrt{2}}{\sqrt{3}}\cdot\dfrac{1}{2}=\dfrac{-\sqrt{3}-\sqrt{2}}{2\sqrt{3}}\)

c: \(sin\left(a-\dfrac{pi}{3}\right)\)

\(=sina\cdot cos\left(\dfrac{pi}{3}\right)-cosa\cdot sin\left(\dfrac{pi}{3}\right)\)

\(=\dfrac{\sqrt{2}}{\sqrt{3}}\cdot\dfrac{1}{2}+\dfrac{1}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{2}=\dfrac{\sqrt{2}+\sqrt{3}}{2\sqrt{3}}\)

d: \(cos\left(a-\dfrac{pi}{6}\right)\)

\(=cosa\cdot cos\left(\dfrac{pi}{6}\right)+sina\cdot sin\left(\dfrac{pi}{6}\right)\)

\(=\dfrac{-1}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{2}+\dfrac{\sqrt{2}}{\sqrt{3}}\cdot\dfrac{1}{2}=\dfrac{-\sqrt{3}+\sqrt{2}}{2\sqrt{3}}\)

1 / (   sin 2   α )   =   1   +   c o t 2   α = 1 + 4/9 = 13/9 ⇒   sin 2   α   =   9 / 13 .

Suy ra sinα = ± 3 / 13 .

Vì π/2 < α < π nên sinα > 0. Vậy sinα =  3 / 13 . .

Từ đó cosα = sinα.cotα = ( - 2 ) / 13 .

Đáp án là A.

\(sin\alpha=-\sqrt{1-cos^2\alpha}=-\dfrac{\sqrt{21}}{5}\)

\(tan\alpha=\dfrac{sin\alpha}{cos\alpha}=\dfrac{-\dfrac{\sqrt{21}}{5}}{-\dfrac{2}{5}}=\dfrac{\sqrt{21}}{2}\)

\(cot\alpha=\dfrac{1}{tan\alpha}=\dfrac{2}{\sqrt{21}}\)

Suy ra 0 < cot α < 1. Vậy các phương án A, B, C bị loại.

Đáp án: D