Sprawdź tożsamość (...), jeżeli (...)
: 16 mar 2008, o 12:42
Sprawdź tożsamość \(\displaystyle{ \frac{\sin\alpha}{1 + \cos\alpha}}\) = \(\displaystyle{ \frac{1}{\sin\alpha}}\) \(\displaystyle{ - \cot\alpha}\), jeżeli \(\displaystyle{ 0}\)
\(\displaystyle{ \frac{sin\alpha}{1 + cos\alpha} = \frac{1}{sin\alpha} - \frac{cos\alpha}{sin\alpha} \\
\frac{sin\alpha}{1 + cos\alpha} = \frac{1 - cos\alpha}{sin\alpha} \\
sin^{2}\alpha = 1 - cos^{2}\alpha \\
sin^{2}\alpha + cos^{2}\alpha = 1 \\
1 = 1}\)