Question

$tan^{-1} \dfrac{1}{\sqrt{x^{2} - 1}}$

Write this in Simplest Form.

Answer 1

Answer:

(π/2) - sec⁻¹x

Step-by-step explanation:

$Given:tan^{-1}(\frac{1}{\sqrt{x^2-1}})$

Put x = secθ ⇒ θ = sec⁻¹x.

Now,

= tan⁻¹(1/√sec²θ - 1)

∴ We know that sec²θ = 1 + tan²θ

= tan⁻¹(1/√tan²θ)

= tan⁻¹(1/tan θ)

= tan⁻¹(cotθ)

= tan⁻¹(tan(90 - θ))

∴ We know that tan⁻¹(tanθ) = θ

= 90 - θ

= (π/2) - sec⁻¹x

Hope it helps!

Answer 2

∴ We know that tan⁻¹(tanθ) = θ

= 90 - θ

= (π/2) - sec⁻¹x

Hope it helps!