Question

sin20+cos40=2sin30cos10左边是如何化为右边的

Answer 1

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