The value of cot x plus cot 60° plus cot 120° is equal to

• A. cot 3x
• B. tan 3x
• C. tan 3x
• D. 3 minus 9 over tan 2x divided by tan x minus tan 3x

To solve the expression involving cotangent, let's break it down step by step.

Understanding Cotangent Values

The cotangent function is the reciprocal of the tangent function. We need to find the values of cot 60° and cot 120° first:

• cot 60°: This is equal to 1/√3 or √3/3.
• cot 120°: This is equal to -1/√3 or -√3/3.

Combining the Values

Now, we can add these values to cot x:

cot x + cot 60° + cot 120° = cot x + (√3/3) + (-√3/3) = cot x.

Final Expression

Thus, the expression simplifies to:

cot x = A.

Identifying the Options

Now, let's analyze the options provided:

• A. cot 3x
• B. tan 3x
• C. tan 3x
• D. 3 - 9/tan 2x divided by (tan x - tan 3x)

Since we found that cot x equals A, the answer is simply:

A. cot 3x