化简:(1)sin2120°+cos180°+tan45°-cos2(-330°)+sin(-210°)(2)sin(θ-5π)cos(-π2-θ)cos(8π-θ)sin(θ-3π2)sin(-θ-

题目简介

化简:(1)sin2120°+cos180°+tan45°-cos2(-330°)+sin(-210°)(2)sin(θ-5π)cos(-π2-θ)cos(8π-θ)sin(θ-3π2)sin(-θ-

题目详情

化简:(1)sin2120°+cos180°+tan45°-cos2(-330°)+sin(-210°)
(2)
sin(θ-5π)cos(-
π
2
-θ)cos(8π-θ)
sin(θ-
2
)sin(-θ-4π)
题型:解答题难度:中档来源:不详

答案

(1)sin2120°+cos180°+tan45°-cos2(-330°)+sin(-210°)
=sin2(180°-60°)-1+1°-cos2(360°-30°)-sin(180°+30°)
=sin260°-1+1-cos230°+sin30°
=(
3
2
)
2
-(
3
2
)
2
+class="stub"1
2

=class="stub"1
2

(2)
sin(θ-5π)cos(-class="stub"π
2
-θ)cos(8π-θ)
sin(θ-class="stub"3π
2
)sin(-θ-4π)

=
(-sinθ)(-sinθ)cosθ
cosθ(-sinθ)

=-sinθ.

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