For which of the following values is \(\tan x\) undefined?
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Answer and explanation
Correct answer: \(x=\frac{(2n+1)\pi}{2},\; n\in\mathbb{Z}\)
\(\tan x=\frac{\sin x}{\cos x}\). It is undefined when \(\cos x=0\), i.e. at \(x=\frac{(2n+1)\pi}{2}\). At \(x=n\pi\), tan equals 0, so option A is not correct. Exam tip: link tan’s domain to non-zero cosine.
Frequently asked questions
What is the correct answer to this question?
\(x=\frac{(2n+1)\pi}{2},\; n\in\mathbb{Z}\)
Why is this the correct answer?
\(\tan x=\frac{\sin x}{\cos x}\). It is undefined when \(\cos x=0\), i.e. at \(x=\frac{(2n+1)\pi}{2}\). At \(x=n\pi\), tan equals 0, so option A is not correct. Exam tip: link tan’s domain to non-zero cosine.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
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