Which of the following trigonometric functions is an odd function?
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Answer and explanation
Correct answer: \(\tan x\)
\(\tan(-x)=\frac{\sin(-x)}{\cos(-x)}=\frac{-\sin x}{\cos x}=-\tan x\); therefore, \(\tan x\) is an odd function. \(\cos x\) and \(\sec x\) are even, and \(\cos^2 x\) is also even. Exam tip: test an odd function using \(f(-x)=-f(x)\).
Frequently asked questions
What is the correct answer to this question?
\(\tan x\)
Why is this the correct answer?
\(\tan(-x)=\frac{\sin(-x)}{\cos(-x)}=\frac{-\sin x}{\cos x}=-\tan x\); therefore, \(\tan x\) is an odd function. \(\cos x\) and \(\sec x\) are even, and \(\cos^2 x\) is also even. Exam tip: test an odd function using \(f(-x)=-f(x)\).
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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