Question

care sunt solutiile ecuatiei : tgx+tg(3x+pi/4)=0 ?

Answer 1

Avem formula $tg(a+b)=\dfrac{\sin(a+b)}{\cos a\cos b}$

Obtinem:
$\dfrac{\sin(x+3x+\dfrac{\pi}{4})}{\cos x\ \cos(3x+\dfrac{\pi}{4})}=0\Rightarrow \sin(4x+\dfrac{\pi}{4})=0$ cu solutiile
$4x_k+\dfrac{\pi}{4}=k\pi,\ k\in Z\Rightarrow x_k=\dfrac{k\pi}{4}-\dfrac{\pi}{16},\ k\in Z.$