> 数学 >
tan(a+
π
4
)=
1
3
,则
(sina−cosa)2
cos2a
=______.
人气:274 ℃ 时间:2020-03-19 03:06:02
解答
∵tan(a+
π
4
)=
tana+1
1−tana
=
1
3

∴tana=-
1
2

因此,
(sina−cosa)2
cos2a
=
sin2a−2sinacosa+cos2a
cos2a−sin2a

分子分母都除以cos2a,得
(sina−cosa)2
cos2a
=
tan2a−2tana+1
1−tan2a
=3
故答案为:3
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