化简;(1)sin(π+α)sin(2π-α)cos(-π-α)sin(3π+α)cos(π-α)cos(3π2+α)(2)cos20°+cos160°+sin1866°-sin(-606°)-数学

题目简介

化简;(1)sin(π+α)sin(2π-α)cos(-π-α)sin(3π+α)cos(π-α)cos(3π2+α)(2)cos20°+cos160°+sin1866°-sin(-606°)-数学

题目详情

化简;
(1)
sin(π+α)sin(2π-α)cos(-π-α)
sin(3π+α)cos(π-α)cos(
2
+α)

(2)cos20°+cos160°+sin1866°-sin(-606°)
题型:解答题难度:中档来源:不详

答案

(1)原式=
-sinα(-sinα)(-cosα)
-sinα(-cosα)sinα
=-1;
(2)原式=cos20°-cos20°+sin(5×360°+66°)-sin(-2×360°+114°)
=sin66°-sin114°
=sin66°-sin(180°-66°)
=sin66°-sin66°
=0.

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