Question

已知tana=2求2sin2a-sinacosa+cos2a-1的值

Answer 1

2sin2a－sinacosa＋cos2a－1
=4sinacosa－sinacosa＋(1－2sin²a)－1
=3sinacosa－2sin²a
=[3sinacosa－2sin²a]/[sin²a＋cos²a] 【分子分母同除以cos²a】
=[3tana－2tan²a]/[1＋tan²a]
=－2/5

Answer 2

tana=sina/cosa=2
sina=2cosa
sin²a+cos²a=1
5cos²a=1
cos²a=1/5
sin²a=4/5

2sin2a-sinacosa+cos2a-1
=2sinacosa-sinacosa+1-2sin²a-1
=sinacosa-2sin²a
=2cos²a-2sin²a
=2/5-8/5
=-6/5

Answer 3

2sin²a-sinacosa+cos²a-1
=sin²a-sinacosa
=(sin²a-sinacosa)/(sin²a+cos²a)
=(tan²a-tana)/(tan²a+1)
=(4-2)/(4+1)
=2/5