Răspuns:
26) 135°
Explicație pas cu pas:
26)
[tex] {( \sin(x) - \cos(x) )}^{2} = 2 \\ { \sin(x) }^{2} + { \cos(x) }^{2} - 2 \sin(x) \cos(x) = 2 \\ 1 - \sin(2x) = 2 \\ \sin(2x) = - 1 \\ x = \frac{3\pi}{4} \\ x = 135[/tex]
27)
[tex] sin^{2} (x+\frac{\pi}{3}) - cos^{2} (x+ \frac{\pi}{3}) \\ = (sin (x+\frac{\pi}{3})+cos(x+\frac{\pi}{3})) \times (sin (x+\frac{\pi}{3}) - cos(x+ \frac{\pi}{3})) \\ = ( \sin(x) \cos( \frac{\pi}{3} ) + \cos(x ) \sin( \frac{\pi}{3} ) + \cos(x) \cos( \frac{\pi}{3} ) - \sin(x) \sin( \frac{\pi}{3} ) ) \times( \sin(x) \cos( \frac{\pi}{3} ) + \cos(x ) \sin( \frac{\pi}{3} ) - \cos(x) \cos( \frac{\pi}{3} ) + \sin(x) \sin( \frac{\pi}{3} ) ) \\ = ( \cos(x) - \sin(x) ) \times ( \cos(x) + \sin(x) ) \\ = \cos^{2} (x) - \sin^{2} (x) \\ = 2 \cos ^{2} (x) - 1 \\ = \cos(2x) [/tex]
