(cosπ/12+sin11π/12)(cosπ/12+sin13π/12)

二分之根号三

(cosπ/12+sin11π/12)(cosπ/12+sin13π/12)
=(cosπ/12+sinπ/12)(cosπ/12-sinπ/12)
=(cosπ/12)^2-(sinπ/12)^2
=cosπ/6
=1/2根号3

=[cosπ/12+sin(π-π/12)][cosπ/12+sin(π+π/12)]
=(cosπ/12+sinπ/12)(cosπ/12-sinπ/12)
=(cosπ/12)^2-(sinπ/12)^2
=cosπ/6
=√3/2

sin11π/12=sinπ/12
sin13π/12=-sinπ/12
所以原式可化为(cosπ/12+sinπ/12)(cosπ/12-sinπ/12)
即(cosπ/12)*cos(π/12)-(sinπ/12)*(sinπ/12)
即：cosπ/6=。。。

(cosπ/12+sin11π/12)(cosπ/12+sin13π/12)
=(cosπ/12+sin1π/12)(cosπ/12-sin1π/12)
=（cosπ/12）^2-(sin1π/12)^2
=cosπ/6
=√3/2