(1)化简:1-2sin100°cos280°1-cos2170°-cos370°.(2)已知:sinαcosα=14,且π4<α<π2,求cosα-sinα的值.-高三数学

题目简介

(1)化简:1-2sin100°cos280°1-cos2170°-cos370°.(2)已知:sinαcosα=14,且π4<α<π2,求cosα-sinα的值.-高三数学

题目详情

(1)化简:
1-2sin100°cos280°
1-cos2170°
-cos370°

(2)已知:sinαcosα=
1
4
,且
π
4
<α<
π
2
,求cosα-sinα的值.
题型:解答题难度:中档来源:不详

答案

(1)原式=
1-2cos10°sin10°
sin210°
-cos10°
=
(cos10°-sin10)2
sin10°-cos10°
=class="stub"cos10°-sin10°
sin10°-cos10°
=1
(2)∵(sinα-cosα)2=sin2α-2sinαcosα+cos2α
=(sin2α+cos2α)-2sinαcosα;
又∵sin2α+cos2α=1,sinαcosα=class="stub"1
4

∴(sinα-cosα)2=1-2×class="stub"1
4
=class="stub"1
2

class="stub"π
4
<α<class="stub"π
2

∴cosα-sinα=-
2
2

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