Published by:
CGP EDU Academic Team
Published on: August 12, 2026
If xy + yz + xz = 1, then prove that 
+ 
+ 
= 
.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Let x = tanA, y = tanB, z = tanC
tan (A + B + C) = 
xy + yz + zx = 1
⇒ 1 – tan A tan B – tanB tanC – tanC tan A = 0
⇒ tan (A + B + C) = does not exist.
⇒ A + B + C = (2n + 1) 
, n ∈ I
So 2A + 2B + 2C = (2n + 1) π
⇒ tan (2A + 2B + 2C) = 0
⇒ tan2A + tan2B + tan 2C = tan 2A tan 2B tan 2C
⇒ 
+ 
+ 
= 
⇒ 
+ 
+ 
= 
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