Simplify: (sin A + cosec A)² + (cos A + sec A)² − (tan²A + cot²A).
सरल कीजिए: (sin A + cosec A)² + (cos A + sec A)² − (tan²A + cot²A)
Answer और ExplanationAnswer and explanation
Answer: (B) 7
(sin A + cosec A)² = sin²A + cosec²A + 2 (क्योंकि sin A cosec A = 1)
(cos A + sec A)² = cos²A + sec²A + 2
योग = (sin²A + cos²A) + 4 + cosec²A + sec²A = 1 + 4 + cosec²A + sec²A
अब tan²A + cot²A घटाएँ: (sec²A − tan²A) + (cosec²A − cot²A) = 1 + 1
कुल = 1 + 4 + 1 + 1 = 7
✓
उत्तर 7 है।
(sin A + cosec A)² = sin²A + cosec²A + 2 (since sin A cosec A = 1)
(cos A + sec A)² = cos²A + sec²A + 2
Sum = (sin²A + cos²A) + 4 + cosec²A + sec²A = 1 + 4 + cosec²A + sec²A
Subtract tan²A + cot²A: (sec²A − tan²A) + (cosec²A − cot²A) = 1 + 1
Total = 1 + 4 + 1 + 1 = 7
✓
The answer is 7.
SMART APPROACH
A = 45° रखें: sin A + cosec A = 1√2 + √2 = 3√2, इसका वर्ग 92 है। cos वाला भाग भी यही है। 92 + 92 − (1 + 1) = 7।
Put A = 45°: sin A + cosec A = 1√2 + √2 = 3√2, whose square is 92. The same for the cos part. 92 + 92 − (1 + 1) = 7.
Source: Selection Post Phase XIV (Graduate) · 17 Sep 2026 · Shift 1। Solution: Prashant Sir, Vijayastra।Source: Selection Post Phase XIV (Graduate) · 17 Sep 2026 · Shift 1. Solution by Prashant Sir, from Vijayastra.