Question

请教一题sin20°的平方+cos50°的平方+sin30°sin70°=?

Answer 1

2 sinA sinB = cos(A-B) - cos(A+B)

sin30°sin70°=cos(30°-70°)-cos(30°+70°)=cos40°-cos100°

sin20°的平方=(1-cos2*20°)/2=(1-cos40°)/2

同理cos50°的平方=(1-cos2*50°)/2=(1-cos100°)/2

原式=(1-cos40°)/2+(1-cos100°)/2+(cos40°-cos100°)/2=1