Question

Enter your answer and show all the steps that you use to solve this problem in the space provided.

Verify the basic identity. What is the domain of validity?

cotθ=cosθcscθ

Answer 1

[AI-generated answer — Bot GPT 3.5]

To verify the basic identity cotθ = cosθcscθ, we need to manipulate the given expression to see if it simplifies to an identity.

First, recall that cotθ = cosθ/sinθ and cscθ = 1/sinθ. Therefore, cosθcscθ = cosθ(1/sinθ) = cosθ/sinθ.

Since cotθ = cosθ/sinθ and cosθ/sinθ = cotθ, we have verified the basic identity cotθ = cosθcscθ.

The domain of validity for this identity is all real numbers except for the values of θ where sinθ = 0, since the division by zero is undefined. Therefore, the domain of validity is all real numbers except for θ such that sinθ = 0.