Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If tan A, tan B are the roots of the quadratic equation
abx 2 – c 2 x + ab = 0, where a, b, c are the sides of a triangle, then –
A
cos C = 0
B
tan A = 
C
tan B = 
D
tan A + tan B = 
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a, b, c, d)
tan A + tan B = c 2 /ab, tan A tan B = 1
⇒ tan (A + B) = 
= ∞
∴ A + B = π /2 ⇒ C = π /2 = cos C = 0.
This is
∴ cos C = 
= 0
⇒ a 2 + b 2 = c 2
⇒ (2 R sin A) 2 + (2 R sin B) 2 = (2 R sin C) 2 ⇒ sin
2 A + sin 2 B + sin 2 C = 2 sin 2 C = 2 [ C = π /2]
tan A + tan B = 
= 
= 
+ 
This is
But tan A tan B = 1 = 
. 
∴ tan A = 
, tan B = 
These are and
Hence , , , are correct answers.
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