Solving Trig Problem: Showing Sin(1/9pi) to Sin(4/9pi)=3/16

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To show that sin(1/9π) sin(2/9π) sin(1/3π) sin(4/9π) equals 3/16, the user initially struggled with various approaches. They attempted to replace sin(2π/9) and sin(3π/9) using the sine addition formula, aiming to factor out sin(π/9). Despite confusion and setbacks, the user ultimately found a solution. The discussion highlights the challenge of using trigonometric identities to simplify the expression effectively. The problem illustrates the complexities of trigonometric equations and the usefulness of sine properties in solving them.
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hey,
i have to show that
\sin \left( 1/9\,\pi \right) \sin \left( 2/9\,\pi \right) \sin \left( <br /> <br /> 1/3\,\pi \right) \sin \left( 4/9\,\pi \right) = 3/16



i ve tried so many things, and i couldn't get to 3/16 :confused: , does anyone have any hints that are going to help me solve problems in that kind!? thanks!
 
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It works for me. What have you done?
 
Well, i have remplaced sin(2pi/9) by sin(3pi/9 - pi/9) and sin(3pi/9) by sin(4pi/9 - pi/9) and so on, and used the relation sin(a+b)=sina cosb + sinb cos a. so everything will have sin(pi/9) in it, so i can factor with that to get something helpful. but i guess i just messed everything up, and i don't know what relation i can use to get closer the 3/16 or what method i should use
 
never mind, i got it :smile:
 

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