Question

Sin30^2+cos60^2+sin30cos60=3/4 Sin20^2+cos50^2+sin20cos50=3/

Answer 1

一般规律的等式：[sinα]^2+[cos(α+30)]^2+sinαcos(α+30)=3/4.

证明：左端=[sinα]^2+[√3/2cosα-1/2sinα]^2+sinα[√3/2cosα-1/2sinα]=[sinα]^2+3/4[cosα]^2+1/4[sinα]^2-1/2[sinα]^2=3/4[sinα]^2+3/4[cosα]^2=3/4.