Simplify: (cosec A − cot A)² + (cosec A + cot A)² − 4 cot²A.
सरल कीजिए: (cosec A − cot A)² + (cosec A + cot A)² − 4 cot²A
Answer और ExplanationAnswer and explanation
Answer: (C) 2
(a − b)² + (a + b)² = 2(a² + b²)
इसलिए (cosec A − cot A)² + (cosec A + cot A)² = 2 cosec²A + 2 cot²A
व्यंजक (Expression) = 2 cosec²A + 2 cot²A − 4 cot²A = 2(cosec²A − cot²A)
= 2 × 1 = 2 (क्योंकि cosec²A − cot²A = 1)
✓
उत्तर 2 है।
(a − b)² + (a + b)² = 2(a² + b²)
So (cosec A − cot A)² + (cosec A + cot A)² = 2 cosec²A + 2 cot²A
Expression = 2 cosec²A + 2 cot²A − 4 cot²A = 2(cosec²A − cot²A)
= 2 × 1 = 2 (since cosec²A − cot²A = 1)
✓
The answer is 2.
SMART APPROACH
A = 45° रखें: (√2 − 1)² + (√2 + 1)² − 4 = (3 − 2√2) + (3 + 2√2) − 4 = 2।
Put A = 45°: (√2 − 1)² + (√2 + 1)² − 4 = (3 − 2√2) + (3 + 2√2) − 4 = 2.
Source: Selection Post Phase XIV (12th) · 19 Sep 2026 · Shift 2। Solution: Prashant Sir, Vijayastra।Source: Selection Post Phase XIV (12th) · 19 Sep 2026 · Shift 2. Solution by Prashant Sir, from Vijayastra.