Question

已知tanα=2,求 3sin²α+3sinαcosα-2cos²α

Answer 1

3(sinα)^2+3sinαcosα-2(cosα)^2

=[3(sinα)^2+3sinαcosα-2(cosα)^2]/[(sinα)^2+(cosα)^2] 分子分母同除(cosα)^2

=[3(tanα)^2+3tanα-2]/[(tanα)^2+!]

=(3*4+3*2-2)/(4+1)

=16/5