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.
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Verify the basic identity. What is the domain of validity?
cotθ=cosθcscθ
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