Question

demonstrati ca cos(a+b)/cosacosb= 1-tgatgb, pentru orice a,b apartine de (0, pi/2)

Answer 1

$\dfrac{\cos (a+b)}{\cos a\cdot \cos b}=\dfrac{\cos a\cdot \cos b-\sin a\cdot \sin b}{\cos a\cdot \cos b}=\dfrac{\cos a\cdot \cos b}{\cos a\cdot \cos b}-\dfrac{\sin a\cdot \sin b}{\cos a\cdot \cos b}=\\ =1-\dfrac{\sin a}{\cos a}\cdot \dfrac{\sin b}{\cos b}=1-tg\ a\cdot tg\ b$