cos方5π/12+cos方π/12+cosπ/12*cos5π/12 最后等于5/4的过程.
问题描述：
cos方5π/12+cos方π/12+cosπ/12*cos5π/12 最后等于5/4的过程.
答
=(1+cos5π/6)/2+(1+cosπ/6)/2+cosπ/12cos(π/2-π/12)
=1+cos5π/6+cosπ/6+cosπ/12sinπ/12
=1-√3/2+√3/2+1/2sinπ/6
=1+1/4
=5/4
答
cos²5π/12+cos²π/12+cosπ/12*cos5π/12
=cos²5π/12+sin²(π/2-π/12)+sin(π/2-π/12)*cos5π/12
=cos²5π/12+sin²5π/12+sin5π/12cos5π/12
=1+ (1/2)sin5π/6
=1+1/4
=5/4
答
cos²5π/12+cos²π/12+cosπ/12*cos5π/12
由于cos5π/12=sin（π/2-5π/12）=sinπ/12
原式=sin²π/12+cos²π/12+cosπ/12sinπ/12
=1+½sinπ/6
=1+1/4
=5/4