化简:(1)sin[α+(2n+1)π]•2sin[α-(2n+1)π]sin(α-2nπ)cos(2nπ-α)(n∈Z)(2)sin(2π-α)sin(π+α)cos(-π-α)sin(3π-α)•

题目简介

化简:(1)sin[α+(2n+1)π]•2sin[α-(2n+1)π]sin(α-2nπ)cos(2nπ-α)(n∈Z)(2)sin(2π-α)sin(π+α)cos(-π-α)sin(3π-α)•

题目详情

化简:(1)
sin[α+(2n+1)π]•2sin[α-(2n+1)π]
sin(α-2nπ)cos(2nπ-α)
(n∈Z)

(2)
sin(2π-α)sin(π+α)cos(-π-α)
sin(3π-α)•cos(π-α)
题型:解答题难度:中档来源:不详

答案

(1)
sin[α+(2n+1)π]•2sin[α-(2n+1)π]
sin(α-2nπ)cos(2nπ-α)
=class="stub"sinα•2sinα
sinαcosα
=2tanα
(2)
sin(2π-α)sin(π+α)cos(-π-α)
sin(3π-α)•cos(π-α)
=class="stub"-sinα•sinα•cosα
-sinα•cosα
=sinα

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