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Question

If sin3 x sin 3x=nm=0cm cos mx where c0,c1,c2.,cn are constants and cn0, then the value of n is


A

15

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B

6

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C

1

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D

0

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Solution

The correct option is B

6


sin3 x sin 3x=14(3 sin xsin 3x)sin 3x=38.2 sin x sin 3x 18.2 sin2 3x=38(cos 2xcos 4x)18(1cos 6x)=18+38 cos 2x38cos 4x+18cos 6x ....(i)

and nm=0cm cos mx=c0+c1 cos x+c2 cos 2x +c3 cos 3x+.....+cn cos nx ......(ii)

Comparing both sides of (i) and (ii), we get n = 6


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