问题 解答题
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)
答案

(1)

sin[α+(2n+1)π]•2sin[α-(2n+1)π]
sin(α-2nπ)cos(2nπ-α)
=
sinα•2sinα
sinαcosα
=2tanα

(2)

sin(2π-α)sin(π+α)cos(-π-α)
sin(3π-α)•cos(π-α)
=
-sinα•sinα•cosα
-sinα•cosα
=sinα

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