If 7 cosec θ – 3 cot θ = 7 where θ is in first quadrant, then the value of 7 cot θ – 3 cosec θ is equal to :यदि 7 cosec θ – 3 cot θ = 7 जहाँ θ प्रथम चतुर्थांश में हो, तो 7 cot θ – 3 cosec θ का मान है :

1. A3
2. B5
3. C3/7
4. D5/7

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Correct answer: A. 3

Explanation

Let c = cosec θ and k = cot θ, with c² - k² = 1. From 7c - 3k = 7 we get c = 1 + 3k/7. Substituting: 1 + 6k/7 + 9k²/49 = 1 + k², so 6/7 = k(1 - 9/49) = 40k/49, giving k = 21/20 and c = 29/20 (check: 29² - 21² = 400 = 20²). Then 7k - 3c = 147/20 - 87/20 = 60/20 = 3. Hence the answer is 3.मान लें c = cosec θ और k = cot θ, जहाँ c² - k² = 1। 7c - 3k = 7 से c = 1 + 3k/7। प्रतिस्थापन करने पर 1 + 6k/7 + 9k²/49 = 1 + k², अतः 6/7 = k(1 - 9/49) = 40k/49, जिससे k = 21/20 और c = 29/20 (जाँच: 29² - 21² = 400 = 20²)। तब 7k - 3c = 147/20 - 87/20 = 60/20 = 3। अतः उत्तर 3 है।