Solution: We have
cos 2x cos(x/2) - cos 3x cos ( 9x/2 )
multiply and divide by 2, we get
1/2 [ 2 cos 2x cos ( x/2) - 2 cos 3x cos ( 9x/2 )]
using the formula ,
2 cos x cos y = cos(x+y) + cos(x-y) , we get ,
=1/2 [ cos ( 2x + x/2 ) - cos ( 2x - x/2 ) - cos ( 3x + 9x / 2 ) + cos ( 3x - 9x/2 )]
= 1/2 [ cos 5x/2 - cos 3x/2 - cos 15x/2 + cos3x/ 2]
= 1/2 [ cos 5x/2 - cos 15x/2]
= 1/2 [ -(- 2 sin 5x sin 5x/2 )]
= sin 5x sin 5x/2
