化简sin^2(20')+cos^2(80')+根号下3*sin20'*cos80'
问题描述：
化简sin^2(20')+cos^2(80')+根号下3*sin20'*cos80'
答
积化和差：√3*sin20cos80 =(√3/2)(sin100-sin60)=(√3/2)sin80-3/4
逆用二倍角公式：
sin²(20)+cos²(80）= (cos80)² + (cos70)²
= (1/2)·[cos160 + 1 + cos140 + 1]
= 1 - (1/2)·(cos40 + cos20)
= 1 - (1/2)·2cos30cos10
= 1 - cos30cos10
= 1- (√3/2)sin80
∴原式 = 1/4