Use the given sum or difference identity to find $\displaystyle {\sin{{\left(\alpha+\beta\right)}}}$  exactly, given that $\displaystyle {\cos{\alpha}}=\frac{{1}}{{6}}$ such that $\displaystyle \alpha$ terminates in quadrant IV and $\displaystyle {\cos{\beta}}=\frac{{4}}{{5}}$ such that $\displaystyle \beta$ terminates in quadrant IV then:

 $\displaystyle {\sin{{\left(\alpha+\beta\right)}}}={\sin{{\left(\alpha\right)}}}{\cos{{\left(\beta\right)}}}+{\cos{{\left(\alpha\right)}}}{\sin{{\left(\beta\right)}}}$ 

 $\displaystyle {\sin{{\left(\alpha+\beta\right)}}}={(}$ $\displaystyle {)}$$\displaystyle {\left(\frac{{4}}{{5}}\right)}$$\displaystyle +{\left(\frac{{1}}{{6}}\right)}$$\displaystyle {(}$ $\displaystyle {)}$ 

 $\displaystyle {\sin{{\left(\alpha+\beta\right)}}}=$

Preview Question 6 Part 3 of 3  

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