Answer :

We are given that,

tan-1 (cot θ) = 2θ


We need to find the value of θ.


We have,


tan-1 (cot θ) = 2θ


Taking tangent on both sides,


tan [tan-1 (cot θ)] = tan 2θ


Using property of inverse trigonometry,


tan(tan-1 A) = A


cot θ = tan 2θ


Or,


tan 2θ = cot θ


Using the trigonometric identity,




Using the trigonometric identity,




By cross-multiplying,


tan θ × 2 tan θ = 1 – tan2 θ


2 tan2 θ = 1 – tan2 θ


2 tan2 θ + tan2 θ = 1


3 tan2 θ = 1




And .



Thus,


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