已知tanα=-1/2,2sin²α+sinα·cosα-3cos²α的值

已知tanα=-1/2,2sin²α+sinα·cosα-3cos²α的值
已知tanα=-1/2,2sin²α+sinα·cosα-3cos²α的值

已知tanα=-1/2,2sin²α+sinα·cosα-3cos²α的值
sin^2α+2sinαcosα-3cos^2α
=（sin^2α+2sinαcosα-3cos^2a)/(sin^2α+cos^2α)
=(tan^2α+2tanα-3)/(tan^2α+1)
=(1/4-1-3)/(1/4+1)
=-15/5
=-3