If a=pi/3 prove that cosacos2acos3acos4acos5acos6a=1/16
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π/3= 60 degree
so cos a= 1/2
cos 2a= cos 120= -1/2
cos 3a =cos 180= -1
cos 4a= cos 240= cos(180+60)= -cos60= -1/2
cos5a= cos300= cos(360-60)= cos60= 1/2
cos 6a =cos360=1
so on multiplying all of them
(1/2)(-1/2)(-1)(-1/2)(1/2)(1)= -1/16
so cos a= 1/2
cos 2a= cos 120= -1/2
cos 3a =cos 180= -1
cos 4a= cos 240= cos(180+60)= -cos60= -1/2
cos5a= cos300= cos(360-60)= cos60= 1/2
cos 6a =cos360=1
so on multiplying all of them
(1/2)(-1/2)(-1)(-1/2)(1/2)(1)= -1/16
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