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Find the number of solutions of the equation | sin(theta) cos(theta + pi/6) sin(2*theta) | | cos(theta + pi/6) cos(theta + 2*pi/3) -sin(2*theta + pi/3) | = 0 | -cos(theta - pi/6) cos(theta - 2*pi/3) sin(2*theta + 2*pi/3) | in the interval [0, 2*pi].
- 2
- 4
- 8
- infinite
Correct answer: infinite
Solution
By applying column operations (such as C3 → C3 + linear combination of C1 and C2) and using sum-product trigonometric identities, the determinant can be shown to equal zero for every value of theta. Hence the equation holds for all theta in [0, 2*pi], giving infinitely many solutions.
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