If (\sin x=\sin y), which relation can generally be true?
Answer and explanation
Correct answer: \(x=2n\pi+y\) or \(x=(2n+1)\pi-y\), where \(n\in\mathbb Z\)
When \(\sin x=\sin y\), the two general families are \(x=2n\pi+y\) and \(x=(2n+1)\pi-y\), where \(n\in\mathbb Z\). The first follows from periodicity, while the second uses \(\sin(\pi-y)=\sin y\). Option B represents only some cases and misses the second family. Exam tip: for equal sine values, remember the angles \(y\) and \(\pi-y\).
Frequently asked questions
What is the correct answer to this question?
\(x=2n\pi+y\) or \(x=(2n+1)\pi-y\), where \(n\in\mathbb Z\)
Why is this the correct answer?
When \(\sin x=\sin y\), the two general families are \(x=2n\pi+y\) and \(x=(2n+1)\pi-y\), where \(n\in\mathbb Z\). The first follows from periodicity, while the second uses \(\sin(\pi-y)=\sin y\). Option B represents only some cases and misses the second family. Exam tip: for equal sine values, remember the angles \(y\) and \(\pi-y\).
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
