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question mark

If sin³xsin3x= ∑Cm cosmx where C0,C1...Cn are constants and Cn≠ 0 then n is
A. 15
B. 6
C. 1
D. 0
Please refer to the attached image as well.

Ushma , 7 Years ago
Grade 11
anser 1 Answers
Arun
Dear student
 
sin^3 x = (3 sinx  – sin3x) / 4
 
also
 
sin ax sinbx = ½ (cos(a – b)x – cos (a+b)x)
 
use the above identities
 
sin^3 x sin3x = (3 sinx  – sin3x) * sin3x / 4
 
 = 3/8 (cos 2x – cos 4x ) – 1/8 (cos 0x – cos 6x)
 
 = 1/8 (cos 6x – 3 cos4x + 3 cos2x – cos 0x)
 
Hence n =6
 
 
Hope it helps
 
Regards
Arun (askIITians forum expert)
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Last Activity: 7 Years ago
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