化简sin（25π/12）cos（11π/6）-cos（11π/12）sin（5π/6）的值是

原式=sin(25π/12-2π)cos(11π/6-2π）-[-cos（π-11π/12）]sin(π-5π/6)
=sin(π/12)cos(-π/6)+cos(π/12)sin(π/6)
=sin(π/12)cos(π/6)+cos(π/12)sin(π/6）
=sin(π/12+π/6)
=sin(π/4)
=√2/2

sin（25π/12）cos（11π/6）-cos（11π/12）sin（5π/6）
=sin（2π+π/12）cos（2π-π/6）-cos（π-π/12）sin（π-π/6）
=sin（π/12）cos（π/6）+cos（π/12）sin（π/6）
=1/2[sin（π/12+π/6）+sin（π/12-π/6）]+1/2[sin（π/12+π/6）-sin（π/12-π/6）]
=1/2[2sin（π/12+π/6）]
=sin（π/12+π/6）
=sin(3π/12)
=sin(π/4)
=√2/2

sin（25π/12）cos（11π/6）-cos（11π/12）sin（5π/6）
=sin（2π+π/12）cos（2π-π/6）-cos（π-π/12）sin（π-π/6）
=sin（π/12）cos（π/6）+cos（π/12）sin（π/6）
=sin（π/12+π/6）
=sin（π/4）
=√2/2

原式=sin（π/12）cosπ/6+cos（π/12）sinπ/6
=sin(π/12+π/6)
=sinπ/4=√2/2