(sin5π/12+cos5π/12)(sinπ/12-cosπ/12)
=[sin(π/2-π/12)+cos(π/2-π/12)](sinπ/12-cosπ/12)
=(cosπ/12+sinπ/12)(sinπ/12-cosπ/12)
=sin²π/12-cos²π/12
=-(cos²π/12-sin²π/12)
=-cosπ/6
=-√3/2