(a)证明：
左边=cos(x-y)-cos(x+y)
=(cosxcosy+sinxsiny)-(cosxcosy-sinxsiny)
=2sinxsiny
=右边
证毕
(b)证明：
由(1)的结论知：
左边=2sinθ(sinθ+sin3θ+sin5θ+sin7θ)
=2sinθsinθ+2sinθsin3θ+2sinθsin5θ+2sinθsin7θ
=[cos(θ-θ)-cos(θ+θ)]+[cos(θ-3θ)-cos(θ+3θ)]+[cos(θ-5θ)-cos(θ+5θ)]+[cos(θ-7θ)-cos(θ+7θ)]
=cos0-cos2θ+cos2θ-cos4θ+cos4θ-cos6θ+cos6θ-cos8θ
=1-cos8θ
=右边
证毕