Question

if cos7x-cos8x/1+2cos5x=cos(ax)-cos(bx) then a²+b² is?​

Answer 1

L.H.S.=cos7x−cos8x1+2cos5x  

=cos7x−cos8x1+2cos5x∗2sin(5x2)2sin(5x2)

=2sin(5x2)cos7x−2sin(5x2)cos8x2sin(5x2)+4sin(5x2)cos5x

=[sin(19x2)−sin(9x2)]−[sin(21x2)−sin(11x2)]2(sin(5x2)+2sin(5x2)cos5x)

=[sin(19x2)+sin(11x2)]−[sin(21x2)+sin(9x2)]2(sin(5x2)+(sin(15x2)−sin(5x2)))

=2sin(15x2)cos2x−2sin(15x2)cos3x2sin(15x2)

=cos2x−cos3x=R.H.S.