Use the given sum or difference identity to find sin⁡(α+β)\displaystyle {\sin{{\left(\alpha+\beta\right)}}} exactly, given that sin⁡α=16\displaystyle {\sin{\alpha}}=\frac{{1}}{{6}} such that α\displaystyle \alpha terminates in quadrant I and sin⁡β=15\displaystyle {\sin{\beta}}=\frac{{1}}{{5}} such that β\displaystyle \beta terminates in quadrant I.

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

 sin⁡(α+β)=(16)(\displaystyle {\sin{{\left(\alpha+\beta\right)}}}={\left(\frac{{1}}{{6}}\right)}{(} )+(\displaystyle {)}+{(} )\displaystyle {)} (15)\displaystyle {\left(\frac{{1}}{{5}}\right)} 

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

 

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

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