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Evaluate the determinant | cos(theta+phi) -sin(theta+phi) cos 2phi | | sin theta cos theta sin phi | | -cos theta sin theta cos phi | Which statement best describes it?
- equals 0
- is independent of theta
- is independent of phi
- is independent of both theta and phi
Correct answer: is independent of theta
Solution
Expanding and using angle-sum identities cancels all theta terms, leaving an expression that depends only on phi; hence the determinant is independent of theta.
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