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Is Q(cos φ) = Q(sin φ) for every angle φ?

Is Q(cos φ) = Q(sin φ) for every angle φ?

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Answer #1

No,its not true.

Consider .

then

and

Now

since the minimal polynomial of has degree 2 over .-----------(1)

but since .-----------------(2)

Thus from (1) and (2) we get that

for all angle .

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