[sin(π/12)+cos(π/12)]^2=[sin(π/12)]^2+2sin(π/12)*cos(π/12)+[cos(π/12)]^2=1+22sin(π/12)*cos(π/12)=1+sin(π/6)=1+1/2=3/2因为sin(π/12)+cos(π/12)>0所以sin(π/12)+cos(π/12)=√(3/2)=√6/2