Prove that cos2x cos(x/2)-cos3x cos(9x/2)=sin5x sin(5x/2)

Asked by Aarthi Vishwanathan | 1st Jun, 2012, 08:40: PM

Expert Answer:

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

Answered by  | 1st Jun, 2012, 11:39: PM

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