We are given that,

We need to find the value of x.

Determinant of 3 × 3 matrices is found as,

So,

Using trigonometric identity,

sin² θ + cos² θ = 1

Since,

⇒ -x³ = 8

⇒ x³ = -8

⇒ x³ = -2 × -2 × -2

Taking cube root on both sides,

⇒ x = -2

Thus, the value of x is -2.