Question

Exprimati ctg(a+b) si ctg(a-b) in functie de ctg a si ctg b.​

Answer 1

Răspuns:

Explicație pas cu pas:

$ctg(a+b)=\dfrac{\cos(a+b)}{\sin(a+b)}=\dfrac{\cos a\cdot\cos b-\sin a\cdot\sin b}{\sin a\cdot\cos b+\cos a\cdot \sin b}=\\=\dfrac{\sin a\cdot\sin b\left(\frac{\cos a}{\sin a}\cdot\frac{\cos b}{\sin b}-1\right)}{\sin a\cdot\sin b\left(\frac{\cos b}{\sin b}+\frac{\cos a}{\sin a}\right)}=\dfrac{ctg~a\cdot ctg~b-1}{ctg~a+ctg~b}$