\(\tan \alpha = \frac{4}{3}\) A \(\sin \alpha = \pm \frac{4}{5}\,\,;\,\,\cos \alpha = \pm \frac{3}{5}\,\,;\,\,\cot \alpha = \frac{3}{4}\) B \(\sin \alpha = \frac{4}{5}\,\,;\,\,\cos \alpha = \frac{3}{5}\,\,;\,\,\cot \alpha = \frac{3}{4}\) C \(\sin \alpha = \pm \frac{3}{5}\,\,;\,\,\cos \alpha = \pm \frac{4}{5}\,\,;\,\,\cot \alpha = \frac{3}{4}\) D \(\sin \alpha = \frac{3}{5}\,\,;\,\,\cos \alpha = \frac{4}{5}\,\,;\,\,\cot \alpha = \frac{3}{4}\)

\(\tan \alpha = \frac{4}{3}\)

A \(\sin \alpha = \pm \frac{4}{5}\,\,;\,\,\cos \alpha = \pm \frac{3}{5}\,\,;\,\,\cot \alpha = \frac{3}{4}\)

B \(\sin \alpha = \frac{4}{5}\,\,;\,\,\cos \alpha = \frac{3}{5}\,\,;\,\,\cot \alpha = \frac{3}{4}\)

C \(\sin \alpha = \pm \frac{3}{5}\,\,;\,\,\cos \alpha = \pm \frac{4}{5}\,\,;\,\,\cot \alpha = \frac{3}{4}\)

D \(\sin \alpha = \frac{3}{5}\,\,;\,\,\cos \alpha = \frac{4}{5}\,\,;\,\,\cot \alpha = \frac{3}{4}\)

Hướng dẫn Chọn đáp án là: B

Phương pháp giải:

Sử dụng công thức lượng giác: \(\left\{ \begin{array}{l}{\sin ^2}\alpha + {\cos ^2}\alpha = 1\\\tan \alpha .\cot \alpha = 1\\1 + {\tan ^2}\alpha = \frac{1}{{{{\cos }^2}\alpha }}\end{array} \right..\)

Lời giải chi tiết:

Ta có: \(0 < \alpha < {90^0}\) \( \Rightarrow \left\{ \begin{array}{l}\sin \alpha > 0\\\cos \alpha > 0\\\tan \alpha > 0\\\cot \alpha > 0\end{array} \right..\)

\(\tan \alpha = \frac{4}{3}\)

* \(\tan \alpha .\cot \alpha = 1\)\( \Leftrightarrow \cot \alpha = 1:tan\alpha = 1:\frac{4}{3} = \frac{3}{4}\)

* \(1 + {\tan ^2}\alpha = \frac{1}{{{{\cos }^2}\alpha }}\)\( \Leftrightarrow 1 + {\left( {\frac{4}{3}} \right)^2} = \frac{1}{{{{\cos }^2}\alpha }}\)\( \Leftrightarrow \frac{1}{{{{\cos }^2}\alpha }} = \frac{{25}}{9}\)\( \Rightarrow {\cos ^2}\alpha = \frac{9}{{25}}\)\( \Rightarrow \cos \alpha = \frac{3}{5}\)

*\({\sin ^2}\alpha + {\cos ^2}\alpha = 1\)\( \Leftrightarrow {\left( {\frac{3}{5}} \right)^2} + {\sin ^2}\alpha = 1\)\( \Leftrightarrow {\sin ^2}\alpha = 1 – \frac{9}{{25}} = \frac{{16}}{{25}}\)\( \Rightarrow \sin \alpha = \frac{4}{5}\)

Chọn B.