Explanation:

To solve the problem, let's consider some basic trigonometric identities and relationships within a triangle:

- We know in a triangle ABC, the angles sum up to p: A + B + C = p.

- Given the equation: sinA - cosB - cosC = 0.

Let's analyze the options, knowing sinA = cos(p/2 - A):

- Option 1: p/6

- For B = p/6, cosB = v3/2. Check if sinA = cosB + cosC holds.

- Option 2: p/4

- For B = p/4, cosB = v2/2. Check if sinA = cosB + cosC holds.

- Option 3: p/3

- For B = p/3, cosB = 1/2. Check if sinA = cosB + cosC holds.

- Option 4: p/2

- For B = p/2, cosB = 0. Check if sinA = cosB + cosC holds.

- If B = p/2, A + C = p/2; thus, sinA = cosC, and the equation is balanced: sinA - 0 - cosC = sinA - cosC = 0.

- Correct Answer: p/2