Wykaż tożsamość trygonometryczną.

[aleswi]

wykaz, ze:
\(\displaystyle{ \frac{1} {sin ^{2} \alpha } -1 = tg ^{-2} \alpha}\)

[matmi]

\(\displaystyle{ \frac{1} {\sin ^{2} \alpha } -1 =\frac{1-\sin^2\alpha} {\sin ^{2} \alpha } =\frac{\cos ^{2} \alpha}{\sin ^{2} \alpha}=\left(\frac{\cos \alpha}{\sin \alpha}\right)^{2}=\left(\frac{\sin \alpha}{\cos \alpha}\right)^{-2}= \tan ^{-2} \alpha}\)

[aleswi]

dzieki