\(cot\alpha = \frac{8}{{15}}\) A \(\tan \alpha = \frac{{15}}{8}\,\,;\,\,\sin \alpha = \frac{{15}}{{17}}\,\,;\,\,\cos \alpha = \frac{8}{{17}}\) B \(\tan \alpha = \pm \frac{{15}}{8}\,\,;\,\,\cos \alpha = \pm \frac{{15}}{{17}}\,\,;\,\,\sin \alpha = \pm \frac{8}{{17}}\) C \(\tan \alpha = \frac{{15}}{8}\,\,;\,\,\cos \alpha = \frac{{15}}{{17}}\,\,;\,\,\sin \alpha = \frac{8}{{17}}\) D \(\tan \alpha = \frac{{15}}{8}\,\,;\,\,\sin \alpha = \pm \frac{{15}}{{17}}\,\,;\,\,\cos \alpha = \pm \frac{8}{{17}}\)

\(cot\alpha = \frac{8}{{15}}\)

A \(\tan \alpha = \frac{{15}}{8}\,\,;\,\,\sin \alpha = \frac{{15}}{{17}}\,\,;\,\,\cos \alpha = \frac{8}{{17}}\)

B \(\tan \alpha = \pm \frac{{15}}{8}\,\,;\,\,\cos \alpha = \pm \frac{{15}}{{17}}\,\,;\,\,\sin \alpha = \pm \frac{8}{{17}}\)

C \(\tan \alpha = \frac{{15}}{8}\,\,;\,\,\cos \alpha = \frac{{15}}{{17}}\,\,;\,\,\sin \alpha = \frac{8}{{17}}\)

D \(\tan \alpha = \frac{{15}}{8}\,\,;\,\,\sin \alpha = \pm \frac{{15}}{{17}}\,\,;\,\,\cos \alpha = \pm \frac{8}{{17}}\)

Hướng dẫn Chọn đáp án là: D

Phương pháp giải:

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

Lời giải chi tiết:

\(cot\alpha = \frac{8}{{15}}\)

* \(\tan \alpha .\cot \alpha = 1 \Leftrightarrow tan\alpha = \frac{1}{{\cot \alpha }} = \frac{1}{{\frac{8}{{15}}}} = \frac{{15}}{8}\)

* \(1 + {\cot ^2}\alpha = \frac{1}{{si{n^2}\alpha }}\)\( \Leftrightarrow 1 + {\left( {\frac{8}{{15}}} \right)^2} = \frac{1}{{si{n^2}\alpha }}\)\( \Leftrightarrow \frac{1}{{si{n^2}\alpha }} = \frac{{289}}{{225}}\)\( \Rightarrow si{n^2}\alpha = \frac{{225}}{{289}}\)\( \Rightarrow sin\alpha = \pm \frac{{15}}{{17}}\)

*\({\sin ^2}\alpha + {\cos ^2}\alpha = 1\)\( \Leftrightarrow {\left( {\frac{{15}}{{17}}} \right)^2} + {\cos ^2}\alpha = 1\)\( \Leftrightarrow {\cos ^2}\alpha = 1 – \frac{{225}}{{289}} = \frac{{64}}{{289}}\)\( \Rightarrow \cos \alpha = \pm \frac{8}{{17}}\)

Chọn D.