4. (5 分) 已知 $\sin a-\cos a=\frac{4}{3}$, 则 $\sin 2 a=(\quad)$
Gaokao · Math · previous-year question
- A.$-\frac{7}{9}$correct
- B.$-\frac{2}{9}$
- C.$\frac{2}{9}$
- D.$\frac{7}{9}$
Answer
A. $-\frac{7}{9}$
Explanation
解: $\because \sin a-\cos a=\frac{4}{3}$, $\therefore \quad(\sin a-\cos a)^{2}=1-2 \sin a \cos a=1-\sin 2 a=\frac{16}{9}$, $\therefore \sin 2 a=-\frac{7}{9}$ 故选: A.
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