Question

Somebody please help.

Select the correct answer.
What is the exact value of cos 105°?

Answer 1

Check the picture below.

`\textit{Sum and Difference Identities} \\\\ cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta) \\\\[-0.35em] ~\dotfill\\\\ cos(105^o)\implies cos(60^o+45^o)\implies cos(60^o)\cdot cos(45^o)-sin(60^o)\cdot sin(45^o) \\\\\\ \cfrac{1}{2}\cdot \cfrac{√(2)}{2}~~ - ~~\cfrac{√(3)}{2}\cdot \cfrac{√(2)}{2}\implies \cfrac{√(2)}{4}~~ - ~~\cfrac{√(6)}{4}\implies {\Large \begin{array}{llll} \cfrac{√(2)-√(6)}{4} \end{array}}`