应用诱导公式化简sin（α—2π）sin（α+π）-2cos（α—π/2）sin（α—π）-cos²（π/2+α）

Question

应用诱导公式化简
sin（α—2π）sin（α+π）-2cos（α—π/2）sin（α—π）-cos²（π/2+α）

Answer 1

sin（α—2π）sin（α+π）-2cos（α—π/2）sin（α—π）-cos²（π/2+α）
=sin[-（2π—α）][-sinα]—2cos（π/2-α）sinα—cos（π/2+α）cos（π/2+α）
=-sin(2π—α）（-sinα）—2（-sinα）sinα—sinαsinα
=（-sinα）（-sinα）+2sin²α—sin²α
=-sin²α+2sin²α—sin²α
=0
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