Question

Find the exact value of cos285 using the fact that 285=330-45

Answer 1

`\bf \textit{Sum and Difference Identities} \\\\ cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta)\\\\ -------------------------------\\\\ cos(285^o) \\\\\\ cos(330^o-45^o)=cos(330^o)cos(45^o)+sin(330^o)sin(45^o) \\\\\\ cos(330^o-45^o)=\left( (√(3))/(2) \right)\left( (√(2))/(2) \right)~~+~~\left( (1)/(2) \right)\left( (√(2))/(2) \right) \\\\\\ cos(330^o-45^o)=\cfrac{√(6)}{4}+\cfrac{√(2)}{4}\implies cos(330^o-45^o)=\cfrac{√(6)+√(2)}{4}`