______化简cos(3k+13π+α)+cos(3k-13π-α)(k∈Z).-数学

题目简介

______化简cos(3k+13π+α)+cos(3k-13π-α)(k∈Z).-数学

题目详情

______化简cos(
3k+1
3
π+α)+cos(
3k-1
3
π-α)(k∈Z).
题型:解答题难度:中档来源:不详

答案

原式=cos[kπ+(class="stub"π
3
+α)]+cos[kπ-(class="stub"π
3
+α)]
=coskπcos(class="stub"π
3
+α)-sinkπsin(class="stub"π
3
+α)+coskπcos(class="stub"π
3
+α)+sinkπsin(class="stub"π
3
+α)
=2coskπcos(class="stub"π
3
+α)
=2(-1)k(cosclass="stub"π
3
cosα-sinclass="stub"π
3
sinα)
=(-1)k(cosα-
3
sinα),k∈Z.

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