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If the determinant | sin²(2x) cos(2x) 4*sin²(x/2) | | tan²(x/2) cos² x - sin² x... | | -2*cos(4x) tan²(x/2) sin(4x) | expands as a0 + a1*cos x + a2*cos² x +... + an*cosⁿ x, find a0 (the constant term, i.e., value at x = 0 in the cos-x polynomial sense).
- 0
- 1
- -1
- 2
Correct answer: 0
Solution
Setting cos x = 0 (x = pi/2) makes several entries vanish, and the determinant evaluates to 0, so the constant term a0 = 0.
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