Question

Evaluate sin105° using the sum and differences identities underdstanding 105°=45°+60°

Answer 1

`\bf \textit{Sum and Difference Identity} \\\\ sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta)\\\\ -------------------------------\\\\ sin(45^o+60^o)\implies sin(45^o)cos(60^o)+cos(45^o)sin(60^o) \\\\\\ \cfrac{√(2)}{2}\cdot \cfrac{1}{2}+\cfrac{√(2)}{2}\cdot \cfrac{√(3)}{2}\implies \cfrac{√(2)}{4}+\cfrac{√(6)}{4}\implies \cfrac{√(2)+√(6)}{4}`

check your Unit Circle for those angles.