Using trigonometric identity, the angle represented by x is: x = 50°
How to solve trigonometric Identity?
The Compound Angle Formula states that the cosine of the sum of two angles is equal to the product of the cosines of the individual angles minus the product of their sines.
In other words,
cos(a + b) = cos(a)cos(b) – sin(a)sin(b).
We are given:
Cos(2x) cos(x) - Sin(2x) Sin(x) = -√3/2
Applying the compound angle formula, we have:
cos (2x + x) = -√3/2
cos (3x) = -√3/2
3x = cos⁻¹(-√3/2)
3x = 150
x = 150/3
x = 50°