tanα=3,求sin2α-cos2α的值

tanα=3,求sin2α-cos2α的值
tanα=3,求sin2α-cos2α的值

tanα=3,求sin2α-cos2α的值
sin2α-cos2α=2sinαcosα-((cosα)^2-(sinα)^2)=2(cosα)^2tanα-(2(cosα)^2-1)
=6/(3^2+1)-2/(3^2+1)+1
=6/10-2/10+1
=7/5
法二
万能公式sin2α=2tanα/1+(tanα)^2=3/5
cos2α=1-(tanα)^2/1+(tanα)^2=-4/5
所以原式=7/5