已知角a为钝角,且sin(a+π/12)=1/3,则cos(a+5π/12)=?

已知角a为钝角,且sin(a+π/12)=1/3,则cos(a+5π/12)=?
已知角a为钝角,且sin(a+π/12)=1/3,则cos(a+5π/12)=?

已知角a为钝角,且sin(a+π/12)=1/3,则cos(a+5π/12)=?
角a为钝角,且sin(a+π/12)=1/3,则a+π/12为钝角,于是cosa(a+π/12)=-（2根2）/3 a+5π/12=a+π/12+π/3
cos（a+5π/12）=cos（a+π/12）cosπ/3-sin(a+π/12)sinπ/3
=-[2（根号2）/3]（1/2）-（1/3）（根号3）/2
=-（根号3+2根号2）/6