高中数学必修 第一册（648题）

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知识点：第五章 三角函数

参考答案：\(\because \left ( {\sin {x-\cos {x}}} \right )^{2}=1-2\cos {x}\sin {x}=\frac {49} {25}\)，

\(\therefore \)\(\sin x - \cos x = \pm \frac{7}{5}\)

\(\because x\)为第四象限角， \(\sin x < 0\) ，\(\cos x > 0\)

\(\therefore \sin {x}-\cos {x}<0，\therefore \sin {x}-\cos {x}=-\frac {7} {5}\)，联立\(\cos {x}+\sin {x}=\frac {1} {5}\)得：\(\left \{ \begin{array}{*{20}{l}} {\sin {x}=-\frac {3} {5}} \\ {\cos {x}=\frac {4} {5}} \end{array} \right .\)

\(\therefore \)\(\tan x = \frac{{\sin x}}{{\cos x}} = - \frac{3}{4}\)．

解析：