求sin20+cos50+sin20cos50的值,

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
这里要用到三个三角函数公式：
sina+sinb=2sin((a+b)/2)cos((a-b)/2
(cosa)^2 =1/2+1/2*cos2a
cos(a)cos(b)=1/2*[cos(a+b)+cos(a-b)]
ok.

求sin20°+cos50°+sin20°cos50°的值
原式=sin20°+sin40°+sin20°sin40°=2sin30°cos10°+(1/2)(cos20°-cos60°)
=cos10°+(1/2)cos20°-1/4=cos10°+(1/2)(2cos²10°-1)-1/4=cos²10°+cos10°-3/4
=(cos10°+1/2)²-1=(0.9848+0.5)²-1=1.2047