(a)

The given value $\"\"$ .

Step 1 :

From cosine value

Hypotenuse = 4

Adjacent = - √6

From Pythagorean theorem

$\"\"$

Formula for sine function : $\"\"$

$\"\"$

Step 2 :

To find value of sin 2θ

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

$\"\"$

Solution :

$\"\"$

(b)

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 2θ

Apply double angle of cos function formula : $\"image\"$

Substitute $\"image\"$ and $\"image\"$ in above formula

$\"image\"$

Solution :

$\"image\"$