Question

Write the following in the simplest form:

`cot^-1  a/sqrt(x^2-a^2),|  x  | > a`

Answer 1

Let x = a sec θ

Now,

`cot^-1  a/sqrt(x^2-a^2)=cot^-1(a/sqrt(a^2sec^2theta-a^2))`

`=cot^-1  a/(asqrt(tan^2theta`

`=cot^-1(cottheta)`

= θ

`=sec^-1  x/a`