Monthly Archives: September 2022

Let $\alpha$, $\beta$, and $\gamma$ be the interior angles of $\triangle{ABC}$. Find all solutions so that $$\cos\alpha\cdot\cos\beta+\sin\alpha\cdot\sin\beta\cdot\sin\gamma=1$$ 🔑 Solution: Since $\alpha$, $\beta$, and $\gamma$ are the interior angles of $\triangle{ABC}$, we have $$0\lt\alpha,\ \beta,\ \gamma\lt\pi$$ Therefore $$0\lt\sin\alpha,\ \sin\beta,\ \sin\gamma\le 1$$ … Continue reading →