Question

The Simplest form of `cot^-1 (1/sqrt(x^2 - 1))`, |x| > 1 is

Options

• tan θ

• cos θ

• sec θ

• sec^–1x

Answer 1

sec^–1x

Explanation:

Let x = sec θ, the

`sqrt(x^2 - 1) = sqrt(sec^2 theta - 1)` = tan θ

Therefore, `cot^-1  1/sqrt(x^2 - 1) = cot^-1 (cot theta)` = θ

= sec^–1x, Which is the simplest form.