tanα=3 时，2sin^2α+sinαcosα-3cos^2α的值是多少？

2sin^2α+sinαcosα-3cos^2α
=1-cos2α+sin2α/2-(3/2+3cos2α/2)
=sin2α/2-5cos2α/2-1/2
=2tanα/[2(1+tan^2α)]-5(1-tan^2α)/[2(1+tan^2α)]-1/2
=3/(1+3^2)-5(1-3^2)/[2(1+3^2)]-1/2
=9/5

先都转化成α的二倍角,再用万能公式

1.sina=3cosa,带入化简
2.(sina)^2+(cosa)^2=1

3.9