Question

Ajutor!E urgent
Dau coroana
i) tg(x+pi\4)=tg(2x-pi/4)
m) tg 4x/3+tg 2x/3=0
o) cos 3x-cos5x=0

Answer 1

Răspuns:

x=$\frac{\pi }{2}+k\pi ;$ k apartine Z

Explicație pas cu pas:

$\tan\left(x+\frac{\pi}{4}\right)=\tan\left(2x-\frac{\pi}{4}\right)=>\tan\left(x+\frac{\pi}{4}\right)=\tan\left(2x-\frac{\pi}{4}\right),\ x$ ≠ $\frac{\pi}{4}$+k$\pi$,  k apartine Z, $x\ne\frac{3\pi}{8}+\frac{k\pi}{2}$ k apartine Z

$\tan\left(x+\frac{\pi}{4}\right)-\tan\left(2x-\frac{\pi}{4}\right)=0=>\\\frac{\sin\left(-x+\frac{\pi}{2}\right)}{\cos\left(x+\frac{\pi}{4}\right)\cos\left(2x+\frac{\pi}{4}\right)}=0=>\\\sin\left(-x+\frac{\pi}{2}\right)=0;\\\ \cos\left(x\right)=0=>x=\frac{\pi}{2}+k\pi$

sau $x=90\ grade\ +k\cdot180grade$