Use the given sum or difference identity to find $\displaystyle {\cos{{\left(\alpha+\beta\right)}}}$  exactly, given that $\displaystyle {\sin{\alpha}}=\frac{{3}}{{4}}$ such that $\displaystyle \alpha$ terminates in quadrant II and $\displaystyle {\cos{\beta}}=-\frac{{1}}{{3}}$ such that $\displaystyle \beta$ terminates in quadrant II then:

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

 $\displaystyle {\cos{{\left(\alpha+\beta\right)}}}={(}$ $\displaystyle {)}$ $\displaystyle {\left(-\frac{{1}}{{3}}\right)}-$ $\displaystyle {\left(\frac{{3}}{{4}}\right)}{(}$ $\displaystyle {)}$ 

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

Preview Question 6 Part 3 of 3  

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