Question

One of the values of x for which `|(cos x, sin x), (- cos x, sin x)|` = 1 is ______.

Options

• 0

• `π/4`

• `π/3`

• `π/2`

Answer 1

One of the values of x for which `|(cos x  sin x), (- cos x  sin x)|` = 1 is `underlinebb(π/4)`.

Explanation:

Determinant = cos⁡ x × sin ⁡x − (−cos ⁡x × sin ⁡x) = 2cos ⁡x sin ⁡x = sin⁡ 2x.

Given sin ⁡2x = 1, so 2x = `π/4`, which matches the correct option.