Răspuns:
Explicație pas cu pas:
Salutare!
Pentru rezolvare, substituim ctgα cu [tex]\frac{cos \alpha}{sin \alpha}[/tex] .
[tex]\frac{cos \alpha + ctg \alpha}{ctg \alpha} = \frac{cos \alpha + \frac{cos \alpha}{sin\alpha} }{\frac{cos \alpha}{sin\alpha}} = \frac{\frac{cos\alpha sin\alpha + cos \alpha}{sin \alpha} }{\frac{cos \alpha}{sin\alpha}} = \frac{cos\alpha sin\alpha + cos \alpha}{sin \alpha}* \frac{sin \alpha}{cos \alpha} = \\\\= \frac{cos\alpha sin\alpha + cos \alpha}{cos\alpha} = \frac{(sin \alpha + 1)cos \alpha}{cos \alpha} = sin \alpha + 1 = 1 + sin \alpha[/tex]
Succes!
