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Prove that: (cos7x-cos8x)/(1+2cos5x)=cos...

Prove that: `(cos7x-cos8x)/(1+2cos5x)=cos2x-cos3x`

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`L.H.S. = (cos7x-cos8x)/(1+2cos5x)`
`= (cos7x-cos8x)/(1+2cos5x)**(2sin((5x)/2))/(2sin((5x)/2))`
`=(2sin((5x)/2)cos7x-2sin((5x)/2)cos8x)/(2sin((5x)/2)+4sin((5x)/2)cos5x)`
`=([sin((19x)/2)-sin((9x)/2)]-[sin((21x)/2)-sin((11x)/2)])/(2(sin((5x)/2)+2sin((5x)/2)cos5x)`
`=([sin((19x)/2)+sin((11x)/2)]-[sin((21x)/2)+sin((9x)/2)])/(2(sin((5x)/2)+(sin((15x)/2) -sin((5x)/2)))`
`=(2sin((15x)/2)cos2x-2sin((15x)/2)cos3x)/(2sin((15x)/2))`
`=cos2x-cos3x = R.H.S.`
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