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山西省2023-2024学年度七年级第一学期阶段性练习(三)3数学.考卷答案试卷答案
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分析由已知可得tanα=3，将sin2α+sinαcosα-2利用弦化切思想，化为$\frac{{tan}^{2}α+tanα}{{tan}^{2}α+1}$-2可得答案．
解答解：∵sinα-3cosα=0，
∴sinα=3cosα，即tanα=3，
∴sin2α+sinαcosα-2=$\frac{{sin}^{2}α+sinαcosα}{{sin}^{2}α+{cos}^{2}α}$-2=$\frac{{tan}^{2}α+tanα}{{tan}^{2}α+1}$-2=$\frac{12}{10}$-2=-$\frac{4}{5}$，
故答案为：-$\frac{4}{5}$．
点评本题考查的知识点是同角三角函数基本关系的运算，弦化切思想，难度中档．
