Question

sin20的平方)+(cos80的平方)+根号3*sin20cos80

详细些，网上的都太快了。求值。

Answer 1

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
望采纳谢谢~~

追问

逆用二倍角公式公式怎么弄的

追答

积化和差公式的逆用啊，你是第几步没看懂

Answer 2

√3*sin20cos80 =(√3/2)(sin100-sin60)=(√3/2)sin80-3/4

sin²(20)+cos²(80）= (cos80)² + (cos70)² 【cos2a=2cos^a-1，cos^a=1/2(cos2a+1)】
= (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

追问

第二步怎么化的

追答

(1/2)·[cos160 + 1 + cos140 + 1]
= (1/2)[cos(180-20) + 1 + cos(180-40 )+ 1]
= 1 - (1/2)·(cos40 + cos20)