Published by:
CGP EDU Academic Team
Published on: August 13, 2026
In a triangle ABC if A = π /4 and tan B tan C = k, then k must satisfy -
A
k 2 – 6k + 1 ≥ 0
B
k 2 – 6k + 1 = 0
C
k 2 – 6k + 1 ≤ 0
D
3 – 2 
< k < 3 + 2 
< k < 3 + 2
Text Solution
Verified by ExpertsThe correct answer is:
A
A = π /4, tan B tan C = k ⇒ B + C = 3 π /4
⇒ tan (B + C) = tan 
⇒ 
= –1 ⇒ tan B + tan C = (k – 1)
Equation x 2 – (k – 1) x + k = 0
whole roots are tan B and tan C
for real vales D ≥ 0 (k – 1) 2 – 4k ≥ 0
⇒ k 2 – 6k + 1 ≥ 0.
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