(d)

The given value $\"image\"$ .

Step 1 :

From cosine function

Hypotenuse = 4

Adjacent = - √6

From Pythagorean theorem

$\"image\"$

Formula for sine function : $\"image\"$

$\"image\"$

Step 2 :

To find value of cos(θ/2)

Apply half angle of sine function formula : $\"\"$

Substitute $\"image\"$ in above formula

$\"image\"$

Rewrite the expression with common denominator.

$\"image\"$

Solution :

$\"image\"$