Question

demonstrati indentitatea
$\frac{ \cos \alpha + ctg \alpha }{ctg \alpha } = 1 + \sin \alpha$
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Answer 1

Răspuns:

Explicație pas cu pas:

Salutare!

Pentru rezolvare, substituim ctgα cu   $\frac{cos \alpha}{sin \alpha}$ .

$\frac{cos \alpha + ctg \alpha}{ctg \alpha} = \frac{cos \alpha + \frac{cos \alpha}{sin\alpha} }{\frac{cos \alpha}{sin\alpha}} = \frac{\frac{cos\alpha sin\alpha + cos \alpha}{sin \alpha} }{\frac{cos \alpha}{sin\alpha}} = \frac{cos\alpha sin\alpha + cos \alpha}{sin \alpha}* \frac{sin \alpha}{cos \alpha} = \\\\= \frac{cos\alpha sin\alpha + cos \alpha}{cos\alpha} = \frac{(sin \alpha + 1)cos \alpha}{cos \alpha} = sin \alpha + 1 = 1 + sin \alpha$

Succes!