What is the simplified value of \(\tan(\pi+x)-\tan(\pi-x)\)?
Answer and explanation
Correct answer: \(2\tan x\)
The period of \(\tan\) is \(\pi\), so \(\tan(\pi+x)=\tan x\). Also, \(\tan(\pi-x)=\tan(-x)=-\tan x\). Hence, \(\tan(\pi+x)-\tan(\pi-x)=\tan x-(-\tan x)=2\tan x\). The value \(-2\tan x\) would result if the order of the two terms were reversed. Exam tip: carefully retain the negative sign in \(\tan(\pi-x)\).
Frequently asked questions
What is the correct answer to this question?
\(2\tan x\)
Why is this the correct answer?
The period of \(\tan\) is \(\pi\), so \(\tan(\pi+x)=\tan x\). Also, \(\tan(\pi-x)=\tan(-x)=-\tan x\). Hence, \(\tan(\pi+x)-\tan(\pi-x)=\tan x-(-\tan x)=2\tan x\). The value \(-2\tan x\) would result if the order of the two terms were reversed. Exam tip: carefully retain the negative sign in \(\tan(\pi-x)\).
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
