त्रिभुज ABC में tan A + tan B + tan C = k है। cot A cot B cot C का मान कितना है?

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NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. 0.5 k
  2. 1/k
  3. 3/k
  4. 1/k3

Answer (Detailed Solution Below)

Option 2 : 1/k
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व्याख्या:

त्रिभुज ABC में, A + B + C = π

⇒ tan(A + B + C) = tanπ = 0

\(\frac{tan A+tan B+ tan C - tan A tan Btan C}{1- tan A.tan B- tan B.tan C - tan C.tan A} = 0\)

tanA. tanB. tanC = tanA + tanB + tanC

cotA. cotB. cotC = \(\frac{1}{tan A+tan B+tan C }\)

= 1/k

∴ विकल्प (b) सही है। 

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