Explanation:

Let’s walk through this step by step:

- Start with the equation:

2cos²? - 1 = 0

2cos²? = 1 ? cos²? = ½ ? cos? = 1/v2 (since ? is acute, cos? is positive)

- Now, sin²? + cos²? = 1 ? sin²? = 1 - ½ = ½ ? sin? = 1/v2

- So, tan? = sin?/cos? = (1/v2)/(1/v2) = 1

cot? = 1/tan? = 1

- You need cot²? - tan²?:

cot²? = 1, tan²? = 1, so cot²? - tan²? = 1 - 1 = 0

Let’s check the options:

- Option 1: 0  — This is correct.

- Option 2: 2 — Nope, we just found 0.

- Option 3: 10/3 — No.

- Option 4: 1 — Not right either.

Answer:

What this means: With the values sorted out, only 0 fits perfectly. No other option makes sense based on the math. There’s no need to overthink, just keep it clear and straightforward.