Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If A > 0, B > 0 and A + B = 
then the maximum value of tan A . tan B is -
A
B
C
3
D
Text Solution
Verified by ExpertsThe correct answer is:
B
When A + B = 60 0 ∴ B = 60 0 – A
∴ tan B = tan (60 0 – A) = 
Now z = tan A tan B
or z = 
= 
where t = tan A
= 
= 0
∴ t = 1/ √ 3
∴ t = tan A = tan 30 0 ∴ B = 60
0 – A = 30 0
The other value is rejected as both A and B are +ive acute angles.
If t < 
, 
= + ive and if t > 
, 
= – ive.
Hence max. when t = 
and max. value = 
.
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