Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If tan –1 y = 4 tan –1 x, find y as a rational function of x. Hence show that tan 
is a root of the equation x 4 – 6x 2 + 1 = 0.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Put x = tan θ , then y = tan 4 θ , so that
tan 2 θ = 
= 
⇒ tan 4 θ = 
= 
⇒ y = 
For θ = 
, we have 4 θ = tan 
= ∞ . Thus the denominator of the fraction on the R.H.S. must vanish. i.e., x = tan θ = tan 
must be such that it satisfies the equation x 4 – 6x 2 + 1 = 0
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