Home/ Questions/Q 419894
Next
In Process
Tushar Arpit Modi
Asked: 2022-11-09T18:59:40+05:30 In:

If `cos^(3)x sin2x=sum_(n=1)^(n) a_(m)sinmx` is an identity in x, then which one of the following is in-correct?
A. `a_(2)=0,a_(3)=3/8`
B. `a_(1)=1/2,n=6`
C. `a_(1)=1/4, n=5`
D. `suma_(m)=3/4`

If `cos^(3)x sin2x=sum_(n=1)^(n) a_(m)sinmx` is an identity in x, then which one of the following is in-correct?
A. `a_(2)=0,a_(3)=3/8`
B. `a_(1)=1/2,n=6`
C. `a_(1)=1/4, n=5`
D. `suma_(m)=3/4`
Parabola
Leave an answer

Leave an answer

Browse

1 Answer

  1. Correct Answer – B
    We have,
    `cos^(3)x sin2x=((cos3x+3 cosx)/(4))sin2x`
    `impliescos^(3)x sin2x=1/4(sin2x cos3x+3sin2xcosx)`
    `impliescos^(3)x sin2x=1/8(sin2x cos 3x+6sin2x cosx)`
    `impliescos^(3)x sin2x=1/8(sin 5xsinx+3 sin3x+3sinx)`
    `thereforecos^(3)x sin2x=underset(m=1)overset(n)(sum)a_(n)sin mx`
    `impliesa_(1)sinx+a_(2)sin2x+…+a_(n)sinnx`
    `=1/4sinx+3/8sin 3x+1/8sin5x`
    `impliesa_(1)=1/4,a_(2)=0,a_(3)=3/8,a_(4)=0,a_(5)=1/8`

    • 0