题目

.11
1,求证sin^2(20°)+cos^(50°)+sin20°cos50°=3/4?
2,求证sin^2(15°)+cos^(45°)+sin15°cos45°=3/4?

提问时间：2021-04-07

答案

sin²20°+cos²50°+sin20°cos50°
=(1-cos40°)/2+(1+cos100°)/2+(1/2)*(sin70°-sin30°)
=(1-cos40°)/2+(1-cos80°)/2+(1/2)*(cos20°-1/2)
=1-(1/2)*(cos40°+cos80°)+(1/2)*(cos20°-1/2)
=1-(cos60°cos20°)+(1/2)cos20°-1/4
=1-(1/2)cos20°+(1/2)cos20°-1/4
=3/4