If θ is an acute angle and cosec θ + cot θ = 4, then find cos θ.
यदि θ न्यूनकोण (Acute angle) है और cosec θ + cot θ = 4, तो cos θ ज्ञात कीजिए।
Answer और ExplanationAnswer and explanation
Answer: (B) 15/17
(cosec θ + cot θ)(cosec θ − cot θ) = cosec²θ − cot²θ = 1, इसलिए cosec θ − cot θ = 14
जोड़ने पर: 2 cosec θ = 4 + 14 = 174 ⇒ cosec θ = 178
घटाने पर: 2 cot θ = 4 − 14 = 154 ⇒ cot θ = 158
cos θ = cot θcosec θ = 158 × 817 = 1517
✓
cos θ = 1517।
(cosec θ + cot θ)(cosec θ − cot θ) = cosec²θ − cot²θ = 1, so cosec θ − cot θ = 14
Adding: 2 cosec θ = 4 + 14 = 174 ⇒ cosec θ = 178
Subtracting: 2 cot θ = 4 − 14 = 154 ⇒ cot θ = 158
cos θ = cot θcosec θ = 158 × 817 = 1517
✓
cos θ = 1517.
SMART APPROACH
यदि cosec θ + cot θ = p है, तो cos θ = p² − 1p² + 1 = 16 − 116 + 1 = 1517।
If cosec θ + cot θ = p, then cos θ = p² − 1p² + 1 = 16 − 116 + 1 = 1517.
Source: Selection Post Phase XIV (12th) · 25 Sep 2026 · Shift 2। Solution: Prashant Sir, Vijayastra।Source: Selection Post Phase XIV (12th) · 25 Sep 2026 · Shift 2. Solution by Prashant Sir, from Vijayastra.