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If tan–1 (cot θ) = 2 θ, then θ =
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,