Răspuns:
Explicație pas cu pas:
vom aplica formulele:
[tex]tgx-tgy=\frac{sin(x-y)}{cosx*cosy},~~~ctgx-ctgy=\frac{sin(y-x)}{sinx*siny}\\f)~~\dfrac{tg(2\alpha -\beta)-tg(\beta-2\alpha }{ctg(\beta -2\alpha )-ctg(2\alpha-\beta)}=\dfrac{sin(2\alpha-\beta -\beta+2\alpha )}{cos(2\alpha-\beta )*cos(\beta-2\alpha) }:\dfrac{sin(2\alpha-\beta-\beta +2\alpha }{sin(\beta-2\alpha )*sin(2\alpha-\beta )} =\dfrac{sin4\alpha }{cos(2\alpha-\beta )*cos(\beta-2\alpha)}*\dfrac{sin(\beta-2\alpha )*sin(2\alpha-\beta )}{sin(4\alpha-2\beta ) }=[/tex][tex]tg(2\alpha-\beta)*tg(\beta-2\alpha)* \dfrac{sin4\alpha }{sin(4\alpha-2\beta) }[/tex]
e posibil la numitor sa fie alte semne la expresia initiala......
