Question

Спростити вираз (на фото)​

Answer 1

Ответ:

$\dfrac{sin\alpha}{1+cos\alpha}$

Объяснение:

$\dfrac{sin2\alpha}{1-cos2\alpha} \cdot \dfrac{1-cos\alpha}{cos\alpha}=\dfrac{2sin\alpha cos\alpha \cdot (1-cos\alpha)}{(1-(2cos^{2}\alpha-1)) \cdot cos\alpha}=\dfrac{2sin\alpha \cdot (1-cos\alpha)}{1-2cos^{2}\alpha+1}=$

$=\dfrac{2sin\alpha \cdot (1-cos\alpha)}{2-2cos^{2}\alpha}=\dfrac{2sin\alpha \cdot (1-cos\alpha)}{2 \cdot (1-cos^{2}\alpha)}=\dfrac{sin\alpha \cdot (1-cos\alpha)}{(1-cos\alpha) \cdot (1+cos\alpha)}=\dfrac{sin\alpha}{1+cos\alpha};$