Question

Question is 15 points

Answer 1

`(\pi)/(12)=(1)/(12)\pi=(4)/(12)\pi-(3)/(12)\pi=(1)/(3)\pi-(1)/(4)\pi\\\\(\pi)/(12)=(\pi)/(3)-(\pi)/(4)`

`\cos(\pi)/(12)=\cos\left((\pi)/(3)-(\pi)/(4)\right)=(*)`

`Use:\ \cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b)`

`(*)=\cos(\pi)/(3)\cos(\pi)/(4)+\sin(\pi)/(3)\sin(\pi)/(4)\\\\=(1)/(2)\cdot(\sqrt2)/(2)+(\sqrt3)/(2)\cdot(\sqrt2)/(2)\\\\=(\sqrt2)/(4)+(\sqrt6)/(4)=(\sqrt2+\sqrt6)/(4)`