Simplify the expression: (sin θ + cosec θ)² + (cos θ + sec θ)² − (tan θ + cot θ)².
व्यंजक (Expression) को सरल कीजिए: (sin θ + cosec θ)² + (cos θ + sec θ)² − (tan θ + cot θ)²
Answer और ExplanationAnswer and explanation
Answer: (A) 5
(sin θ + cosec θ)² + (cos θ + sec θ)² = (sin²θ + cos²θ) + 4 + cosec²θ + sec²θ = 5 + cosec²θ + sec²θ
(tan θ + cot θ)² = tan²θ + cot²θ + 2 (क्योंकि tan θ cot θ = 1)
अंतर = 5 + (sec²θ − tan²θ) + (cosec²θ − cot²θ) − 2 = 5 + 1 + 1 − 2 = 5
✓
उत्तर 5 है।
(sin θ + cosec θ)² + (cos θ + sec θ)² = (sin²θ + cos²θ) + 4 + cosec²θ + sec²θ = 5 + cosec²θ + sec²θ
(tan θ + cot θ)² = tan²θ + cot²θ + 2 (since tan θ cot θ = 1)
Difference = 5 + (sec²θ − tan²θ) + (cosec²θ − cot²θ) − 2 = 5 + 1 + 1 − 2 = 5
✓
The answer is 5.
SMART APPROACH
θ = 45° रखें: 92 + 92 − (1 + 1)² = 9 − 4 = 5।
Put θ = 45°: 92 + 92 − (1 + 1)² = 9 − 4 = 5.
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.