Question

Please Help Me. Use an identity to find the exact value of each expression: Note: You are not allowed to use decimals in your answer. sin(96∘)cos(264∘)+cos(96∘)sin(264∘)= and sin⁡(258∘)cos⁡(33∘)−cos⁡(258∘)sin⁡(33∘)=

Answer 1

`\bf \textit{Sum and Difference Identities} \\ \quad \\ sin({{ \alpha}} + {{ \beta}})=sin({{ \alpha}})cos({{ \beta}}) + cos({{ \alpha}})sin({{ \beta}}) \\ \quad \\ sin({{ \alpha}} - {{ \beta}})=sin({{ \alpha}})cos({{ \beta}})- cos({{ \alpha}})sin({{ \beta}}) \\ \quad \\ cos({{ \alpha}} + {{ \beta}})= cos({{ \alpha}})cos({{ \beta}})- sin({{ \alpha}})sin({{ \beta}}) \\ \quad \\ cos({{ \alpha}} - {{ \beta}})= cos({{ \alpha}})cos({{ \beta}}) + sin({{ \alpha}})sin({{ \beta}})\\\\ -------------------------------`


`\bf sin(96^o)cos(264^o)+cos(96^o)sin(264^o)\implies sin(96^o+264^o) \\\\\\ sin(360^o)\implies 0\\\\ -------------------------------\\\\ sin(258^o)cos(33^o)-cos(258^o)sin(33^o)\implies sin(258^o-33^o) \\\\\\ sin(225^o)\implies -\cfrac{√(2)}{2}`