cotα+cotβ=a, tanα+tanβ=b এবং α+β =θ হলে cot θ  এর মান কত?

দেওয়া আছে,

\(\cot \alpha + \cot \beta = a\)

\(\tan \alpha + \tan \beta = b\)

এবং \(\alpha + \beta = \theta\)

আমরা জানি,

\(\cot \theta = \cot (\alpha + \beta) = \frac{\cot \alpha \cot \beta - 1}{\cot \alpha + \cot \beta}\) 🚀

এখন,

\(\tan \alpha + \tan \beta = b\)

\(\frac{1}{\cot \alpha} + \frac{1}{\cot \beta} = b\)

\(\frac{\cot \beta + \cot \alpha}{\cot \alpha \cot \beta} = b\)

\(\frac{a}{\cot \alpha \cot \beta} = b\)

\(\cot \alpha \cot \beta = \frac{a}{b}\) 💡

সুতরাং,

\(\cot \theta = \frac{\frac{a}{b} - 1}{a}\)

\(\cot \theta = \frac{a - b}{ab}\)

\(\cot \theta = \frac{1}{b} - \frac{1}{a}\) 🎉