(1)求值sin2120°+cos180°+tan45°-cos2(-330°)+sin(-210°)(2)化简:sin(α-2π)cos(α-π2)cos(π+α)sin(3π-α)sin(-π-α

题目简介

(1)求值sin2120°+cos180°+tan45°-cos2(-330°)+sin(-210°)(2)化简:sin(α-2π)cos(α-π2)cos(π+α)sin(3π-α)sin(-π-α

题目详情

(1)求值sin2120°+cos180°+tan45°-cos2(-330°)+sin(-210°)
(2)化简:
sin(α-2π)cos(α-
π
2
)cos(π+α)
sin(3π-α)sin(-π-α)
题型:解答题难度:中档来源:不详

答案

(1)sin2120°+cos180°+tan45°-cos2(-330°)+sin(-210°)
=(sin60°)2-cos(0°)+tan45°-(cos30°)2+sin(30°)
=class="stub"3
4
+(-1)+1-class="stub"3
4
+class="stub"1
2

=class="stub"1
2

(2)
sin(α-2π)cos(α-class="stub"π
2
)cos(π+α)
sin(3π-α)sin(-π-α)

=
-sin2αcosα
sin2α

=-cosα

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