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How many different real values of x in the interval −π/4 ≤ x ≤ π/4 satisfy | sin x cos x cos x | | cos x sin x cos x | = 0 | cos x cos x sin x | ?

1. 0
2. 2
3. 1
4. 3

Correct answer: 1

Solution

This is a matrix with diagonal sin x and all off-diagonals cos x, so its determinant is (sin x - cos x)^2 (sin x + 2 cos x) = 0. In [-pi/4, pi/4], sin x = cos x gives x = pi/4, and tan x = -2 lies outside the interval. So exactly 1 solution.

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