In a triangle ABC tan A + tan B + tan C = k  What is the value of cot A cot B cot C? 

This question was previously asked in
NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
View all NDA Papers >
  1. 0.5 k
  2. 1/k
  3. 3/k
  4. 1/k3

Answer (Detailed Solution Below)

Option 2 : 1/k
Free
BSF HC RO/RM All India Mega Live Test
5.4 K Users
100 Questions 200 Marks 120 Mins

Detailed Solution

Download Solution PDF

Explanation:

In triangle ABC, 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

∴ Option (b) is correct

Latest NDA Updates

Last updated on May 30, 2025

->UPSC has released UPSC NDA 2 Notification on 28th May 2025 announcing the NDA 2 vacancies.

-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.

->The NDA exam date 2025 has been announced for cycle 2. The written examination will be held on 14th September 2025.

-> Earlier, the UPSC NDA 1 Exam Result has been released on the official website.

-> The selection process for the NDA exam includes a Written Exam and SSB Interview.

-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100. 

-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential. 

Get Free Access Now
Hot Links: teen patti master 2023 teen patti circle teen patti vip master teen patti teen patti go