What is \(\tan(2\pi-x)\) equal to?
Answer and explanation
Correct answer: \(-\tan x\)
The angles \(2\pi-x\) and \(-x\) are coterminal because they differ by \(2\pi\). Hence, \(\tan(2\pi-x)=\tan(-x)\). Since tangent is an odd function, \(\tan(-x)=-\tan x\). The \(\cot x\) option is incorrect because tangent changes to cotangent for complementary angles, not for this angle. Exam tip: First reduce \(2\pi-x\) to \(-x\).
Frequently asked questions
What is the correct answer to this question?
\(-\tan x\)
Why is this the correct answer?
The angles \(2\pi-x\) and \(-x\) are coterminal because they differ by \(2\pi\). Hence, \(\tan(2\pi-x)=\tan(-x)\). Since tangent is an odd function, \(\tan(-x)=-\tan x\). The \(\cot x\) option is incorrect because tangent changes to cotangent for complementary angles, not for this angle. Exam tip: First reduce \(2\pi-x\) to \(-x\).
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
