Question

(sin x - cos x)² = 0,5 — sin x cos x ​

Answer 1

$( \sin(x) - \cos(x) {)}^{2} = 0.5 - sin(x) \cos(x) \\ \sin ^{2} (x) - 2 \sin(x) \cos(x) + \cos ^{2} (x) = 0.5 - \sin(x) \cos(x) \\ 1 - 2 \sin(x) \cos(x) = 0.5 - \sin(x) \cos(x) \\ sin(x) \cos(x) = \frac{1}{2} \\ \frac{1}{2} \sin(2x) = \frac{1}{2} \\ \sin(2x) = 1 \\ 2x = \arcsin(1) + 2\pi n \\ \\ x = \frac{\pi}{4} + \pi n \: \: \: \: \: n ∈z$