Simplify: cosec Acosec A − 1 + cosec Acosec A + 1.
सरल कीजिए: cosec Acosec A − 1 + cosec Acosec A + 1
Answer और ExplanationAnswer and explanation
Answer: (A) 2 sec²A
LCM लेने पर: cosec A × (cosec A + 1) + (cosec A − 1)cosec²A − 1 = 2 cosec²Acosec²A − 1
cosec²A − 1 = cot²A, इसलिए व्यंजक (Expression) = 2 cosec²Acot²A
= 2 × 1sin²A × sin²Acos²A = 2cos²A = 2 sec²A
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उत्तर 2 sec²A है।
Take the LCM: cosec A × (cosec A + 1) + (cosec A − 1)cosec²A − 1 = 2 cosec²Acosec²A − 1
cosec²A − 1 = cot²A, so the expression = 2 cosec²Acot²A
= 2 × 1sin²A × sin²Acos²A = 2cos²A = 2 sec²A
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The answer is 2 sec²A.
SMART APPROACH
A = 30° रखें, cosec A = 2: 21 + 23 = 83। अब 2 sec²30° = 2 × 43 = 83। इसलिए 2 sec²A।
Put A = 30°, cosec A = 2: 21 + 23 = 83. Now 2 sec²30° = 2 × 43 = 83. So 2 sec²A.
Source: Selection Post Phase XIV (12th) · 23 Sep 2026 · Shift 2। Solution: Prashant Sir, Vijayastra।Source: Selection Post Phase XIV (12th) · 23 Sep 2026 · Shift 2. Solution by Prashant Sir, from Vijayastra.