Use the given sum or difference identity to find $\displaystyle {\cos{{\left(\alpha+\beta\right)}}}$ exactly, given that $\displaystyle {\sin{\alpha}}=-\frac{{2}}{{5}}$ such that $\displaystyle \alpha$ terminates in quadrant III and $\displaystyle {\sin{\beta}}=\frac{{1}}{{4}}$ such that $\displaystyle \beta$ terminates in quadrant I.

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

 $\displaystyle {\cos{{\left(\alpha+\beta\right)}}}={(}$ $\displaystyle {)}{(}$ $\displaystyle {)}-$ $\displaystyle {\left(-\frac{{2}}{{5}}\right)}{\left(\frac{{1}}{{4}}\right)}$ 

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

Preview Question 6 Part 3 of 3  

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