Question

. If tan-1 x - cot -1 x = π/6 then x is

Answer 1

Answer:

The answer is

$\sqrt{3}$

Step-by-step explanation:

The answer is explained in the image.

Answer 2

Answer:

Final Answer.

Step-by-step explanation:

Given,

$tan^{-1}$x - $cot^{-1}$x = π/6

$tan^{-1}$x = π/6 + $cot^{-1}$x

From the relation $tan^{-1}$x + $cot^{-1}$x = π/2

We replace $cot^{-1}$x by π/2 - $tan^{-1}$x.

⇒ $tan^{-1}$x = π/6 + π/2 - $tan^{-1}$x

⇒ 2$tan^{-1}$x = 4π/6

⇒ 2$tan^{-1}$x = 2π/3

⇒ $tan^{-1}$x = π/3

⇒ x = tan(π/3)

tan π/3 = $\sqrt{3}$

Therefore, x = $\sqrt{3}$

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