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Question: How can I evaluate trigonometric expressions in terms of radicals?

Question:How can I evaluate trigonometric expressions in terms of radicals?

mvms271091 90 Maple 2021
pi do-loop
January 13 2022
2

In relation with the following code and its respective output:

I want get an output in wicht left side of equalitys be expressed in radical terms and not in terms of trigonometric expressions. I tried convert(expr, radical), but the result is not that I want. Could someone help me please? Also I want to know if exists a method to avoid hardcoding list of the forloop other than [seq(i, i = 1..5)];

Thank you for helping me;
Greetings;
Lic. Marcus Vinicio Mora Salas;
Chemist;
postgraduate student in University of Costa Rica
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