SOLUTION: Show that 2sin 4pi/5 cos pi/5 = sin 2pi/5

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Question 1142055: Show that
2sin 4pi/5 cos pi/5 = sin 2pi/5
Answer by ikleyn(53762) About Me  (Show Source):
You can put this solution on YOUR website!
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First use the identity  


    sin%28pi-alpha%29 = sin%28alpha%29,


which is valid for any angle alpha.  From this identity, you get


    sin%284pi%2F5%29 = sin%28pi%2F5%29.


It gives you


    2%2Asin%284pi%2F5%29%2Acos%28pi%2F5%29 = 2%2Asin%28pi%2F5%29%2Acos%28pi%2F5%29.


Next use the identity  2%2Asin%28alpha%29%2Acos%28alpha%29 = sin%282%2Aalpha%29,  which is valid for any angle  alpha.  It gives you


    2%2Asin%284pi%2F5%29%2Acos%28pi%2F5%29 = 2%2Asin%28pi%2F5%29%2Acos%28pi%2F5%29 = sin%282pi%2F5%29.


It is what has to be proved.