What is the simplified value of \(\sin(\pi+x)+\sin(\pi-x)\)?
Answer and explanation
Correct answer: \(0\)
Using allied-angle identities, \(\sin(\pi+x)=-\sin x\) and \(\sin(\pi-x)=\sin x\). Therefore, \(\sin(\pi+x)+\sin(\pi-x)=-\sin x+\sin x=0\). The result \(2\sin x\) would occur only if both terms had the same sign, which they do not here. Exam tip: for angles of the form \(\pi\pm x\), determine the sign by identifying the quadrant.
Frequently asked questions
What is the correct answer to this question?
\(0\)
Why is this the correct answer?
Using allied-angle identities, \(\sin(\pi+x)=-\sin x\) and \(\sin(\pi-x)=\sin x\). Therefore, \(\sin(\pi+x)+\sin(\pi-x)=-\sin x+\sin x=0\). The result \(2\sin x\) would occur only if both terms had the same sign, which they do not here. Exam tip: for angles of the form \(\pi\pm x\), determine the sign by identifying the quadrant.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
