Monday, October 31, 2011

Product of Multiple Trignometry Function



PMTF.ID.1:   Product of multiple sine

Proof

(1)

(2)

(3)

(4)
from (3) and (4) ,


(5)


(6)

from (6) and (5)

(7)


(8)
 
(9)

(10)

(11)

(12)
the equation (12) is represented as product of zeros , shown as following

(13)



(14)
from (12) and (14)

(15)

(16)
if x=1 , then


(17)
from (17) and (9)


(18)

(19)


PMTF.ID.1:   Product of multiple cosine




Proof


 
 (1)

 (2)
 
 (3)

 .
 .
 .
 .
  
 (4)

  (5)

 (6)