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Question

Evaluate (cos5x+cos4x)12cos3xdx

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Solution

Given:
(cos5x+cos4x)12cos3xdxsolution;cosC+cosD=2cos(C+D2)cos(CD2)cos5x+cos4x=2cos(9x2)cos(x2)12cos3x=12(2cos23x21)=34cos23x2=3cos3x24cos33x2cos3x2=(4cos33x23cos3x2)cos3x2=cos(3×3x2)cos3x2cos5x+cos4x12cos3x=2cos9x2cosx2cos(9x2)/cos(3x2)=2cosx2cos3x2=(cos(3x2x2)+cos(3x2+x2))=(cosx+cos2x)2(cos+cos2x)dx=(2sinx+sin2x)+C

Hence the correct answer is=(2sinx+sin2x)+C

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