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Question

If sin3xsin3x=m=0nCmcosmx where c0,c1,c2,..cn are constants and Cn0, then the value of n is:


A

2

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B

4

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C

6

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D

8

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Solution

The correct option is C

6


Explanation for the correct option.

Given that, sin3xsin3x=m=0nCmcosmx....(1)

Using sin3x=3sinx-4sin3x & substituting in equation (1) we get:

sin3xsin3x=3sinx-sin3x4sin3x=143sinxsin3x-sin23x=1432[cos4x-cos2x]-sin23xsina+sinb=cosa+b-cos(a-b)=1432[cos4x-cos2x]+cos6x-1=18[3cos4x-3cos2x+2cos6x-2]=18[-2-3cos2x+3cos4x+2cos6x]=m=0nCmcosmx

On comparing the LHS & RHS we get :

n=6

Hence, option (C) is correct.


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