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Step-by-Step Solution
Key Concept: Expand the determinant or use row/column operations to simplify the expression. The result will be independent of \theta.
Expanding the determinant: <br> \Delta = cos(\theta+\phi)(cos\theta cos\phi - sin\theta sin\phi) + sin(\theta+\phi)(sin\theta cos\phi + cos\theta sin\phi) + cos2\phi(sin^2\theta + cos^2\theta) <br> \Delta = cos(\theta+\phi)cos(\theta+\phi) + sin(\theta+\phi)sin(\theta+\phi) + cos2\phi <br> \Delta = cos^2(\theta+\phi) + sin^2(\theta+\phi) + cos2\phi <br> \Delta = 1 + cos2\phi. <br> Since the result is 1 + cos2\phi, it is independent of \theta.
Correct Answer: (B)