Question

С объяснением пожалуйста!

Answer 1

$\sin(x) - \cos(x) = 1 \\ \frac{ \sqrt{2} }{2} ( \sin(x) - \cos(x) ) = \frac{ \sqrt{2} }{2} \\ \frac{ \sqrt{2} }{2} \sin(x) - \frac{ \sqrt{2} }{2} \cos(x) = \frac{ \sqrt{2} }{2} \\ \sin(x) \cos( \frac{\pi}{4} ) - \cos(x) \sin( \frac{\pi}{4} ) = \frac{ \sqrt{2} }{2} \\ \sin(x - \frac{\pi}{4} ) = \frac{ \sqrt{2} }{2} \\ x - \frac{\pi}{4} = ( - 1)^{n} \frac{\pi}{4} + \pi n \\ x = ( - 1)^{n} \frac{\pi}{4} + \frac{\pi}{4} + \pi n, \: n \in Z$