What is the simplified value of \(\cos(\pi+x)+\cos(\pi-x)\)?
Answer and explanation
Correct answer: \(-2\cos x\)
Using allied-angle identities, \(\cos(\pi+x)=-\cos x\) and \(\cos(\pi-x)=-\cos x\). Hence, \(\cos(\pi+x)+\cos(\pi-x)=-\cos x-\cos x=-2\cos x\). The value \(0\) may occur only for particular values such as when \(\cos x=0\); it is not the general simplified form. Exam tip: For angles of the form \(\pi\pm x\), first check the sign of the trigonometric function.
Frequently asked questions
What is the correct answer to this question?
\(-2\cos x\)
Why is this the correct answer?
Using allied-angle identities, \(\cos(\pi+x)=-\cos x\) and \(\cos(\pi-x)=-\cos x\). Hence, \(\cos(\pi+x)+\cos(\pi-x)=-\cos x-\cos x=-2\cos x\). The value \(0\) may occur only for particular values such as when \(\cos x=0\); it is not the general simplified form. Exam tip: For angles of the form \(\pi\pm x\), first check the sign of the trigonometric function.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
