SOLUTION

Given:

cos(x) = sin(60°) * sin(30°) + cos(60°) * cos(30°)

We know the following trigonometric values:

• sin(60°) = √3/2
• cos(60°) = 1/2
• sin(30°) = 1/2
• cos(30°) = √3/2

Substituting these values into the equation:

cos(x) = (√3/2) * (1/2) + (1/2) * (√3/2)

Simplifying:

cos(x) = √3/4 + √3/4

cos(x) = 2√3/4

cos(x) = √3/2

Now, we need to find the angle x whose cosine is √3/2.

From the unit circle or trigonometric table, we know that:

cos(30°) = √3/2

Therefore,

x = 30°