证明题:sin(-α)sin(丌-α) -tan(-α)cot(α-丌)-2cos^2 (-α)+1=sin^2 α
问题描述：
证明题:sin(-α)sin(丌-α) -tan(-α)cot(α-丌)-2cos^2 (-α)+1=sin^2 α
答
sin（π-α）=sinα ∴sin(-α)sin(丌-α)=—sin^2(α)
tan(-α)cot(α-丌)=—1
2cos^2 (-α)=2cos^2 (α)
∴左边=—sin^2(α)+1—2cos^2 (α)+1=1—cos^2 (α)=sin^2(α) =右边
答
sin(-α)sin(丌-α) -tan(-α)cot(α-丌)-2cos^2 (-α)+1
=-sin²α+1-2cos²α+1
=-sin²α+2-2cos²α
=sin²α+2sin²α
=sin²α
得证