Question

Daca x apartine (0, pi/2) si cosx radical2/2, aratati...​

Answer 1

Explicație pas cu pas:

$x \in \left( 0; \frac{\pi}{2}\right); \cos(x) = \frac{\sqrt{2} }{2} = > x = \frac{\pi}{4} \\ = > \sin(x) = \frac{\sqrt{2} }{2}$

$\sin^{2} (x) - 2\sin(x) \cos(x) + \cos^{2} (x) \\ = (sin(x) - \cos(x))^{2} = \left( \frac{ \sqrt{2} }{2} - \frac{ \sqrt{2} }{2} \right)^{2} = 0$

q.e.d.