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Kąt \( \alpha \) jest ostry. \(\sin \alpha +\tg \alpha = \frac{32}{15} \) i \(\sin \alpha -\tg \alpha = - \frac{8}{15} \). Oblicz \(\cos \alpha \)

\(+\underline{\begin{cases}\sin \alpha +\tg \alpha = \frac{32}{15}\\ \sin \alpha -\tg \alpha = - \frac{8}{15}\end{cases}}\\
2\sin\alpha={24\over15}\\ \sin\alpha={4\over5}\)
oraz
\(-\underline{\begin{cases}\sin \alpha +\tg \alpha = \frac{32}{15}\\ \sin \alpha -\tg \alpha = - \frac{8}{15}\end{cases}}\\
2\tg\alpha={40\over15}\\ \tg\alpha={4\over3}\)
czyli
\(\frac{{4\over5}}{\cos\alpha}={4\over3}\iff\cos\alpha={3\over5}\)

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