A) \[\frac{1}{2}\left[ \cos \left( 2x+n\frac{\pi }{2} \right)-\cos \left( 4x+n\frac{\pi }{2} \right) \right]\]
B) \[\frac{1}{2}\left[ {{2}^{n\,\,}}\cos \left( 2x+n\frac{\pi }{2} \right)-{{4}^{n}}\cos \left( 4x+n\frac{\pi }{2} \right) \right]\]
C) \[\frac{1}{2}\left[ {{4}^{n}}\cos \left( 4x+n\frac{\pi }{2} \right)-{{2}^{n}}\cos \left( 2x+n\frac{\pi }{2} \right) \right]\]
D) None of these
Correct Answer: B
Solution :
\[\sin x\sin 3x=\frac{1}{2}[\cos 2x-\cos 4x]\].
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