Cho sin a = 3/ 5 , 0 ∘ < a < 90 ∘ . Tính E = (cot a + tan a)/( cot a − tan a) .

Chọn A

Ta có \(1 + {\cot ^2}a = \frac{1}{{{{\sin }^2}a}} \Rightarrow {\cot ^2}a = \frac{1}{{{{\sin }^2}a}} - 1 = \frac{{25}}{9} - 1 = \frac{{16}}{9}.\)

\(E = \frac{{\cot a + \tan a}}{{\cot a - \tan a}} = \frac{{{{\cot }^2}a + 1}}{{{{\cot }^2}a - 1}} = \frac{{\frac{{16}}{9} + 1}}{{\frac{{16}}{9} - 1}} = \frac{{25}}{9} \cdot \frac{9}{7} = \frac{{25}}{7}.\)