sin^2 10°+ sin^2 50°+ sin10°sin50°

问题描述:

sin^2 10°+ sin^2 50°+ sin10°sin50°
计算 ,

3/4.sin^2 10°+ sin^2 50°+ sin10°sin50°=(1-cos20)/2+(1-cos100)/2+(cos40-cos60)/2=(2-cos20-cos60+cos100+cos40)/2=(2-cos20-cos60+2cos60cos20)/2=(2-cos20-cos60+cos20)/2=(2-1/2)/2=3/4