Răspuns:
x=[tex]\frac{\pi }{2}+k\pi ;[/tex] k apartine Z
Explicație pas cu pas:
[tex]\tan\left(x+\frac{\pi}{4}\right)=\tan\left(2x-\frac{\pi}{4}\right)=>\tan\left(x+\frac{\pi}{4}\right)=\tan\left(2x-\frac{\pi}{4}\right),\ x[/tex] ≠ [tex]\frac{\pi}{4}[/tex]+k[tex]\pi[/tex], k apartine Z, [tex]x\ne\frac{3\pi}{8}+\frac{k\pi}{2}[/tex] k apartine Z
[tex]\tan\left(x+\frac{\pi}{4}\right)-\tan\left(2x-\frac{\pi}{4}\right)=0=>\\\frac{\sin\left(-x+\frac{\pi}{2}\right)}{\cos\left(x+\frac{\pi}{4}\right)\cos\left(2x+\frac{\pi}{4}\right)}=0=>\\\sin\left(-x+\frac{\pi}{2}\right)=0;\\\ \cos\left(x\right)=0=>x=\frac{\pi}{2}+k\pi[/tex]
sau [tex]x=90\ grade\ +k\cdot180grade[/tex]
