求sin20+cos50+sin20cos50的值,
问题描述：
求sin20+cos50+sin20cos50的值,
答
把20换成30-10 50换成60-10展开后可以抵消
答
sin^2 20+cos^2 50+sin20cos50
=(sin20+cos50)^2-sin20cos50
=(sin20+sin40)^2-sin20cos50
=(2sin30*cos(-10))^2-sin20cos50
=cos10^2-sin20cos50
=(1+cos20)/2-1/2*[sin70+sin(-30)]
=1/2+1/2*cos20-1/2*[cos20+sin(-30)]
=1/2+1/4
=3/4