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evaluate integrand sin(3x)cos(4x)cos(7x)
I = sin3x.cos4x.cos7xdx =1/2 [sin3x(2cos4xcos7x)]dx (2cosacosb = cosa+b+ cosa-b ) =1/2[sin3x(cos11x + cos3x)]dx =1/4[2sin3xcos11x +2sin3xcos3x]dx (2sinacosb = sina+b + sina-b) =1/4[sin14x - sin8x + sin6x]dx =1/4 [-cos14x/14 + cos8x/8 - cos6x/6] + c
I = sin3x.cos4x.cos7xdx
=1/2 [sin3x(2cos4xcos7x)]dx (2cosacosb = cosa+b+ cosa-b )
=1/2[sin3x(cos11x + cos3x)]dx
=1/4[2sin3xcos11x +2sin3xcos3x]dx (2sinacosb = sina+b + sina-b)
=1/4[sin14x - sin8x + sin6x]dx
=1/4 [-cos14x/14 + cos8x/8 - cos6x/6] + c
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