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\frac { \operatorname { sin } x + \operatorname { sin } 3 x + \operatorname { sin } 5 x + \operatorname { sin } 7 x } { \operatorname { cos } x + \operatorname { cos } 3 x + \operatorname { cos } 5 x + \operatorname { cos } 7 x } = |
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Answer» numerator = sinx+sin3x+sin5x+sin7x= (sin7x+sinx)+(sin5x+sin3x)= 2sin(7x+x)/2.cos(7x-x)/2+2sin(5x+3x)/2co... [ sinC+sinD=2sin(C+D)/2cos(C-D)/2= 2sin4x.cos3x+2sin4x.cosx= 2sin4x[cos3x+cosx]dinominator = cosx+cos3x+cos5x+cos7x= (cos7x=cosx)+cos5x+cos3x)= 2cos(7x+x)/2.cos(7x-x)/2+2cos(5x+3x)/2.c... [cosC+cosD = 2cos(C+D)/2cos(C-D)/2= 2cos4x.cos3x+2cos4x.cosx= 2cos4x[cos3x+cosx]Numerator/Dinominator= 2sin4x[cos3x+cosx]/2cos4x[cos3x+cosx]= sin4x/cos4x= tan4x |
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