Question

Verify the basic identity. What is the domain of validity?cotθ=cosθcscθ show all work in short terms

Answer 1

[AI-generated answer — Bot GPT 3.5]

To verify the identity cotθ = cosθcscθ, we will use the definition of cotangent and cosecant:

cotθ = cosθ/sinθ
cscθ = 1/sinθ

Now, substitute cscθ into the original identity:

cotθ = cosθ * cscθ
cotθ = cosθ * (1/sinθ)
cotθ = cosθ/sinθ

Since cotθ = cosθ/sinθ, the identity is verified.

The domain of validity for this identity is all real numbers except where sinθ = 0 (i.e., θ = kπ where k is an integer).