Use the given sum or difference identity to find cos(α+β)\displaystyle {\cos{{\left(\alpha+\beta\right)}}}  exactly, given that cosα=58\displaystyle {\cos{\alpha}}=\frac{{5}}{{8}} such that α\displaystyle \alpha terminates in quadrant IV and sinβ=16\displaystyle {\sin{\beta}}=-\frac{{1}}{{6}} such that β\displaystyle \beta terminates in quadrant III then:

 cos(α+β)=cos(α)cos(β)sin(α)sin(β)\displaystyle {\cos{{\left(\alpha+\beta\right)}}}={\cos{{\left(\alpha\right)}}}{\cos{{\left(\beta\right)}}}-{\sin{{\left(\alpha\right)}}}{\sin{{\left(\beta\right)}}} 

 cos(α+β)=(58)(\displaystyle {\cos{{\left(\alpha+\beta\right)}}}={\left(\frac{{5}}{{8}}\right)}{(} )(\displaystyle {)}-{(} )\displaystyle {)} (16)\displaystyle {\left(-\frac{{1}}{{6}}\right)} 

 cos(α+β)=\displaystyle {\cos{{\left(\alpha+\beta\right)}}}=

 

Your answers should be exact but you do not have to rationalize your denominators.