∵2sina-cosa/sina+3cosa=-5
∴分子分母同除以cosa得:(2tana-1)/(tana+3)=-5
解得:tana=-2
∴3sin2a-7cos2a=6sinacosa-7cos²a+7sin²a=(6tana-7+7tan²a)/(tan²a+1)=9/5
∵2sina-cosa/sina+3cosa=-5
∴分子分母同除以cosa得:(2tana-1)/(tana+3)=-5
解得:tana=-2
∴3sin2a-7cos2a=6sinacosa-7cos²a+7sin²a=(6tana-7+7tan²a)/(tan²a+1)=9/5