Question:
What is \(\sin 3x + \cos 3x + 4\sin^3 x – 3\sin x + 3\cos x – 4\cos^3 x\) equal to?
\(\sin 3x + \cos 3x + 4\sin^3 x – 3\sin x + 3\cos x – 4\cos^3 x\) किसके बराबर है?
Options:
- 4 cos 4x
- 0
- 2 sin 2x
- 1
- 4 cos 4x
- 0
- 2 sin 2x
- 1
Correct Answer: b)
Explanation:
Using identities \(\sin 3x = 3\sin x – 4\sin^3 x\) and \(\cos 3x = 4\cos^3 x – 3\cos x\):
\(\sin 3x + 4\sin^3 x – 3\sin x = 0\)
\(\cos 3x – 4\cos^3 x + 3\cos x = 0\)
Sum = \(0 + 0 = 0\).
सर्वसमिका \(\sin 3x = 3\sin x – 4\sin^3 x\) तथा \(\cos 3x = 4\cos^3 x – 3\cos x\) से:
पद परस्पर निरस्त होकर \(0\) प्राप्त होता है।