Which is the correct expansion of (\sin 3x)?
Answer and explanation
Correct answer: \(3\sin x-4\sin^3 x\)
The standard triple-angle identity is \(\sin 3x=3\sin x-4\sin^3 x\), so option B is correct. Option C is the negative of option B and hence equals \(-\sin 3x\). Option D is related to the triple-angle formula for cosine, not sine. Exam tip: remember that the \(\sin^3 x\) term in \(\sin 3x\) has coefficient 4 and a minus sign.
Frequently asked questions
What is the correct answer to this question?
\(3\sin x-4\sin^3 x\)
Why is this the correct answer?
The standard triple-angle identity is \(\sin 3x=3\sin x-4\sin^3 x\), so option B is correct. Option C is the negative of option B and hence equals \(-\sin 3x\). Option D is related to the triple-angle formula for cosine, not sine. Exam tip: remember that the \(\sin^3 x\) term in \(\sin 3x\) has coefficient 4 and a minus sign.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
