If $\sin\alpha = \frac{4}{5}$ and $\alpha \in \left(0,\frac{\pi}{2}\right)$, then find $\frac{1-\cot\alpha}{1+\cot\alpha} = ?$

Question

Accepted Answer

1/7. Since $\sin\alpha=\frac{4}{5}$ and $\alpha$ is acute, $\cos\alpha=\frac{3}{5}$. Thus $\cot\alpha=\frac{\cos\alpha}{\sin\alpha}=\frac{3}{4}$, and substituting gives $\frac{1-3/4}{1+3/4}=\frac{1/4}{7/4}=\frac{1}{7}$.

If $\sin\alpha = \frac{4}{5}$ and $\alpha \in \left(0,\frac{\pi}{2}\right)$, then find $\frac{1-\cot\alpha}{1+\cot\alpha} = ?$

Solution

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