化简:sin[(k+1)π+θ]×cos[(k+1)π-θ] / sin(kπ-θ)×cos(kπ+θ) (k∈Z)

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化简:sin[(k+1)π+θ]×cos[(k+1)π-θ] / sin(kπ-θ)×cos(kπ+θ) (k∈Z)
化简:sin[(k+1)π+θ]×cos[(k+1)π-θ] / sin(kπ-θ)×cos(kπ+θ) (k∈Z)

化简:sin[(k+1)π+θ]×cos[(k+1)π-θ] / sin(kπ-θ)×cos(kπ+θ) (k∈Z)
k为奇数 sin(kπ-θ)×cos(kπ+θ)=-sinθcosθ
sin[(k+1)π+θ]×cos[(k+1)π-θ] =sinθcosθ
k为偶数 sin(kπ-θ)×cos(kπ+θ)=-sinθcosθ
sin[(k+1)π+θ]×cos[(k+1)π-θ] =sinθcosθ
因此
sin[(k+1)π+θ]×cos[(k+1)π-θ] / sin(kπ-θ)×cos(kπ+θ)=-1