Question

How do I write an expression for (1 + cot(theta)) / cot(theta) and simplify it? A) cot(theta) + 1 / cot(theta) B) 1 + cot(theta) / cot(theta) C) 1 / cot(theta) + 1 D) cot(theta) + 1

Answer 1

The expression (1+ cot(theta))/ cot(theta) simplifies to (tan(theta) + 1), because cotangent is the inverse function of tangent and any number divided by itself equals 1.

Step-by-step explanation:

To simplify the expression (1 + cot(theta)) / cot(theta), you first need to understand that cotangent, denoted as cot(theta), is the reciprocal of the tangent function tan(theta), meaning cot(theta) = 1/tan(theta).

So, divided each term in the numerator by cot(theta) individually:

• 1/cot(theta)
• + cot(theta)/cot(theta)

Now simplify the expression:

• 1/cot(theta) becomes tan(theta) (from the definition of cotangent)
• cot(theta)/cot(theta) simplifies to 1 (any number divided by itself equals 1).

Hence, the simplified form of the expression (1 + cot(theta)) / cot(theta) is tan(theta) + 1. So, the correct answer from the given options is not listed.

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