To verify the basic identity cotθ = cosθcscθ, we can rewrite the right side of the equation in terms of sine and cosine functions.
cotθ = cosθ / sinθ
cosθcscθ = cosθ * 1/sinθ = cosθ / sinθ
Since both expressions are equal, the basic identity cotθ = cosθcscθ is verified.
The domain of validity for this identity is all real numbers excluding the points where sinθ = 0, as division by zero is undefined. Therefore, the domain of validity is all real numbers except nπ where n is an integer.
Verify the basic identity. What is the domain of validity?
cotθ=cosθcscθ
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