求:sin^220+cos^280+根号3sin20*cos80的值

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求:sin^220+cos^280+根号3sin20*cos80的值求:sin^220+cos^280+根号3sin20*cos80的值求:sin^220+cos^280+根号3sin20*cos80

求:sin^220+cos^280+根号3sin20*cos80的值
求:sin^220+cos^280+根号3sin20*cos80的值

求:sin^220+cos^280+根号3sin20*cos80的值
题目有误?

sin²20°+cos²80°
= (1 - cos40°)/2 + (1 + cos160°)/2
= 1 + (cos160°- cos40°)/2
= 1 - sin[(160°+ 40°)/2]*sin[(160°- 40°)/2]
= 1 - sin100°sin60°
= 1 - √3/2*sin100°
...

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sin²20°+cos²80°
= (1 - cos40°)/2 + (1 + cos160°)/2
= 1 + (cos160°- cos40°)/2
= 1 - sin[(160°+ 40°)/2]*sin[(160°- 40°)/2]
= 1 - sin100°sin60°
= 1 - √3/2*sin100°
√3sin20°cos80°
= √3/2*(sin100°-sin60°)
= √3/2*sin100°- 3/4
sin²20°+cos²80°+√3sin20°cos80°
= 1 - 3/4 = 0.25

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