Whats up! Im new here. I was trying to demonstrate that the trigonometric ratios of every single integer grade can be written in function of roots. There is a table of trigonometric ratios of multiples of 3 in function of roots. So, if I get to figure out the exact trigonometric ratios of 1 grade, i will have got the trigonometric ratios of all the integers, by addition. I used the ecuation cos (3a) = 4cos3 (a) - 3cos (a) . All I have to do, is call a=1 and do the operations. But, in order to simplify the operations, I supposed a=20, since cos (60) = 0.5. And in order to solve this ecuation for cos (a), I used the first Cardano-Vieta s formula, as trigonometric ratios are real numbers, and in the two other ecuations there is an i.

And finally, I get this ecuation

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How can I remove i? Im sure I havent had a mistake, because the calculator says its right.

Thank you all and sorry for my bad grammar, Im Spanish.