Question

Question #ac2da

Answer 1

No such `theta` exists.

Explanation:

It is an identity that `cos^2(theta) + sin^2(theta) = 1` for all `theta`, thus no `theta` will result in the given equality.

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In the real numbers, there is also the reasoning that
`-1<=cos(theta)<=1` and `-1<=sin(theta)<=1`
`=>`
`0 <= cos^2(theta) <= 1` and `0<=sin^2(theta)<=1`.

Then, even if we allow different angles, for any `theta, gamma in RR` (the real numbers):

`cos^2(theta)+sin^2(gamma) <= 1+1 = 2`

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Even if we allow for complex arguments, however, which allow for greater values of sine and cosine, the original identity still holds, meaning there is still no `theta` fulfilling `cos^2(theta)+sin^2(theta)=3`.