2sinatana=2sin²a/cosa=3
sin²a=3cosa/2
cos²a+sin²a=cos²a+3cosa/2=1
整理,得
2cos²a+3cosa-2=0
(cosa+2)(2cosa-1)=0
cosa=-2(舍去)或cosa=1/2
cos²a=1/4
sin²a=(3/2)(1/2)=3/4
(sina)^4-(cosa)^4
=(sin²a+cos²a)(sin²a-cos²a)
=sin²a-cos²a
=3/4-1/4
=1/2