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Find values of theta in (-pi/4, pi/2) and A in [0, pi/2] satisfying the determinant equation | (1+sin² A) cos² A 2 sin 4theta; sin² A (1+cos² A) 2 sin 4theta; sin² A cos² A (1+2 sin 4theta) | = 0.

1. A = pi/4, theta = -pi/8
2. A = 3pi/8 = theta
3. A = pi/5, theta = -pi/8
4. A = pi/6, theta = 3pi/8

Correct answer: A = pi/4, theta = -pi/8

Solution

Row reduction collapses the determinant to 2 + 2 sin 4theta = 0, so sin 4theta = -1, giving 4theta = -pi/2, theta = -pi/8 (A may be any allowed value such as pi/4).

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