Question

Rút gọn

A = \(\frac{cot+tan}{cot-tan}\) khi sin =\(\frac{3}{5}\),0<a<\(\frac{\pi}{2}\)

Answer 1

Lời giải:

\(\sin a=\frac{3}{5}\Rightarrow \cos ^2a=1-\sin ^2a=\frac{16}{25}\)

Mà \(a\in (0; \frac{\pi}{2})\Rightarrow \cos a>0\). Do đó \(\cos a=\frac{4}{5}\).

\(\Rightarrow \tan a=\frac{\sin a}{\cos a}=\frac{3}{5}: \frac{4}{5}=\frac{3}{4}\Rightarrow \cot a=\frac{1}{\tan a}=\frac{4}{3}\)

Như vậy:

\(A=\frac{\cot a+\tan a}{\cot a-\tan a}=\frac{\frac{4}{3}+\frac{3}{4}}{\frac{4}{3}-\frac{3}{4}}=\frac{25}{7}\)