Given:
There are given that the cos function:

Step-by-step explanation:
To find the value, first, we need to use the half-angle formula:
So,
From the half-angle formula:

Then,
Since 105 degrees is the 2nd quadrant so cosine is negative
Then,
By the formula:

Then,
Put the value of cos210 degrees into the above function:
So,
![\begin{gathered} cos(105^(\circ))=-\sqrt{(1+cos(210))/(2)} \\ cos(105^{\operatorname{\circ}})=-\sqrt{(1-(√(3))/(2))/(2)} \\ cos(105^(\circ))=-\sqrt{(2-√(3))/(4)} \\ cos(105^(\circ))=-\frac{\sqrt{2-√(3)}}{2} \end{gathered}]()
Final answer:
Hence, the value of the cos(105) is shown below:
![cos(105^{\operatorname{\circ}})=-\frac{\sqrt{2-√(3)}}{2}]()