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Given that sin3xsin3x=∑nm=0Cmcosmx,Cn≠0 is an identity. Find the value of n.

Given that sin3xsin3x=∑nm=0Cmcosmx,Cn≠0 is an identity. Find the value of n.

Grade:11

1 Answers

Arun
25763 Points
3 years ago
Dear Shubham
 
Using identity
sin³x = [3 sinx - sin3x]/4
Now
Sin³x sin3x = (3 sinx - sin3x) * sin3x /4
= 3/4 sinx sin3x - sin² 3x/4
= (3/8) ( cos 8x - cos4x) - (1/8) ( cos 0x - cos 6x)
= (1/8) ( cos 6x - 3 cos4x + 3 cos 2x - cos 0x)
Hence n = 6

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