Question

已知tana=2,求sin^2 a-2sinacosa+3cos^2a的值

RT,这是老师抄的题，可是我总觉得怪怪的，好像解不出来。似乎把2sinacosa改成sinacosa比较合适，谁帮忙算下，是不是这题本身就是错误的

Answer 1

答案是0.6
sin^2 a-2sinacosa+3cos^2a
=（sin^2 a-2sinacosa+3cos^2a）/(sin^2a+cos^2a) (因为sin^2a+cos^2a=1)
=（tan^2a-2tana+3）/(tan^2a+1)
=(2*2-2*2+3)/(2*2+1)
=0.6

Answer 2

sin^2 a-2sinacosa+3cos^2a
=(sin^2 a-2sinacosa+3cos^2a)/(sin^2a+cos^2a)
=[(tana)^2-2tana+3]/[(tana)^2+1]
=(4-4+3)/(4+1)
=3/5