উত্তর সিলেক্ট করলে সঠিক ও ভুল দেখাবে।
ব্যাখ্যা ও সঠিক সমাধান
উত্তর:
1/a - 1/b
cotθ = cot(α+β) = (cotαcotβ - 1) / (cotα + cotβ). tanα+tanβ = b => (sinαcosβ + cosαsinβ) / (cosαcosβ) = b => sin(α+β) / (cosαcosβ) = b. cotα+cotβ = a => sin(α+β) / (sinαsinβ) = a. cotαcotβ = sin²(α+β) / (ab). cotθ = (sin²θ/ab - 1) / a = (sin²θ - ab) / a²b. Actually, cotθ = (1 - tanαtanβ) / (tanα+tanβ) = (1 - tanαtanβ) / b. Since cotα+cotβ = a, (tanα+tanβ)/(tanαtanβ) = a => tanαtanβ = b/a. cotθ = (1 - b/a) / b = (a-b)/ab = 1/b - 1/a. Wait, the correct form is 1/b - 1/a.