已知tanα=3,求2(sinα)^2-3cosαcosα的值

题目

已知tanα=3,求2(sinα)^2-3cosαcosα的值

答案

2(sinα)^2-3cosαcosα
=[2(sinα)^2-3cosαcosα]/((sinα)^2+(cosα)^2
=2(tanα)^2-3/ [(tanα)^2+1]
=2*3^2-3/(3^2+1)
=3/2