Rozwiąż tożsamość.
a) 1+ \cot\alpha= \frac{\sin \alpha+ \cos \alpha}{\sin \alpha}
b) \tan \alpha + \cot \alpha= \frac{1}{\sin \alpha* \cos \alpha}
źródło:
przymiotnik
1+\cot\alpha=\frac{\cos\alpha}{\cos\alpha}+\frac{\cos\alpha}{\sin\alpha}=\frac{\cos\alpha\sin\alpha+\cos^2\alpha}{\cos\alpha\sin\alpha}=\frac{\cos\alpha(\sin\alpha+\cos\alpha)}{\cos\alpha\sin\alpha}=\frac{\sin\alpha+\cos\alpha}{\sin\alpha}
\frac{1}{\sin \alpha* \cos \alpha}=\frac{\sin^2 \alpha+ \cos ^2\alpha}{\sin \alpha* \cos \alpha}=\frac{\sin^2 \alpha}{\sin \alpha* \cos \alpha}+\frac{\cos ^2\alpha}{\sin \alpha* \cos \alpha}=\frac{\sin \alpha}{\cos \alpha}+\frac{\cos \alpha}{\sin \alpha}=\tan\alpha+\cot\alpha