cos²(50°+α)+cos²(40°-α)-tan(30°-α)tan(60°+α)=?

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cos²(50°+α)+cos²(40°-α)-tan(30°-α)tan(60°+α)=?cos²(50°+α)+cos²(40°-α)-tan(30°-α)

cos²(50°+α)+cos²(40°-α)-tan(30°-α)tan(60°+α)=?
cos²(50°+α)+cos²(40°-α)-tan(30°-α)tan(60°+α)=?

cos²(50°+α)+cos²(40°-α)-tan(30°-α)tan(60°+α)=?
tan(30°-α)=cot[90°-(30°-α)]=cot(60°+α)
tan(30°-α)tan(60°+α)=cot(60°+α)tan(60°+α)=1
同理:cos2(40°-α)=sin2[90°-(40°-α)]=sin2(50°+α)
cos2(50°+α)+cos2(40°-α)=cos2(50°+α)+sin2(50°+α)=1
1-1=0