If tan^-1(cot θ) = 2 θ, then θ = A. ±π/3 B. ± π/4 C. ±π/6 D. none of these

Question

If tan^-1(cot θ) = 2 θ, then θ =

A.  \(\pm\frac{\pi}3\)

B. \(\pm\frac{\pi}4\)

C. \(\pm\frac{\pi}6\)

D. none of these

Answer 1

Correct answer is C. \(\pm\frac{\pi}6\) 

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,

Thus

θ = \(\pm\frac{\pi}6\)