已知2sina+cosa/sina-3cosa=-5,求3cos2a+4sin2a的值

已知2sina+cosa/sina-3cosa=-5,求3cos2a+4sin2a的值
已知2sina+cosa/sina-3cosa=-5,求3cos2a+4sin2a的值

已知2sina+cosa/sina-3cosa=-5,求3cos2a+4sin2a的值
2sina+cosa=-5sina+15cosa
7sina=14cosa
sina=2cosa
sina²+cosa²=1
5cos²a=1
cos²a=1/5
3cos2a+4sin2a
=3(2cos²a-1)+8sinacosa
=6cos²a-3+16cos²a
=22cosa²-3
=22/5-3
=7/5