If ∫cos4xdx=Ax+Bsin2x+Csin4x+D, then {A,B,C} equals
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a
{38,132,14}
b
{38,14,132}
c
{132,14,38}
d
{14,38,132}
answer is B.
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Detailed Solution
∵∫cos4x=14∫(2cos2x)2dx=14∫(1+cos2x)2dx =14∫(1+2cos2x+cos22x)dx =18∫(2+4cos2x+(1+cos4x))dx =18{3x+2sin2x+14sin4x}+D =38x+14sin2x+132sin4x+D On comparing, we get A=38,B=14,C=132