Which of the following statements is correct about the domain of the function \(f(x)=\tan x\)?
Answer and explanation
Correct answer: It is defined for all real \(x\) except \(x=\frac{(2n+1)\pi}{2}\), where \(n\in\mathbb{Z}\).
Since \(\tan x=\frac{\sin x}{\cos x}\), it is undefined wherever \(\cos x=0\). This occurs at \(x=\frac{(2n+1)\pi}{2}\). Option C excludes zeros of sine, which affect cotangent instead. Exam tip: check the denominator first.
Frequently asked questions
What is the correct answer to this question?
It is defined for all real \(x\) except \(x=\frac{(2n+1)\pi}{2}\), where \(n\in\mathbb{Z}\).
Why is this the correct answer?
Since \(\tan x=\frac{\sin x}{\cos x}\), it is undefined wherever \(\cos x=0\). This occurs at \(x=\frac{(2n+1)\pi}{2}\). Option C excludes zeros of sine, which affect cotangent instead. Exam tip: check the denominator first.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
