Use the given information to find the exact value of the expression.

sin α =21/29 , α lies in quadrant iv, and cos β =-4/11 , β lies in quadrant iii find cos(α+β).

Hello,

sin α =21/29 and α lies in quadrant IV ==>cos α =√(1²-(21/29)²)=20/29.

cos β =-4/11 , β lies in quadrant III ==> sin β =-√(1²-(4/11)²)=-√105 /11

cos(α+β)=cos α cos β- sin α sin β
=20/29*(-4/11)+21/29*√105 / 11 
=(-80+21√105)/(11*29)