tanα=3 时,2sin^2α+sinαcosα-3cos^2α的值是多少?
问题描述：
tanα=3 时,2sin^2α+sinαcosα-3cos^2α的值是多少?
答
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...