求值(1)sin2840°+cos540°+tan225°-cos(-330°)+sin(-210°)(2)已知tanβ=12,求sin2β-3sinβcosβ+4cos2β的值.-数学

题目简介

求值(1)sin2840°+cos540°+tan225°-cos(-330°)+sin(-210°)(2)已知tanβ=12,求sin2β-3sinβcosβ+4cos2β的值.-数学

题目详情

求值
(1)sin2840°+cos540°+tan225°-cos(-330°)+sin(-210°)
(2)已知tanβ=
1
2
,求sin2β-3sinβcosβ+4cos2β的值.
题型:解答题难度:中档来源:不详

答案

(1)∵sin2840°+cos540°+tan225°-cos(-330°)+sin(-210°)
=sin2120°+cos180°+tan45°-cos30°+sin150°
=class="stub"3
4
-1+1-
3
2
+class="stub"1
2

=
5-2
3
4

(2)∵tanβ=class="stub"1
2

∴sin2β-3sinβcosβ+4cos2β
=
sin2β-3sinβcosβ+4cos2β
sin2β+cos2β

=
tan2β-3tanβ+4
tan2β+1

=class="stub"11
5

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