Question

Find the value of the following:

`cos(sec^-1x+\text(cosec)^-1x),` | x | ≥ 1

Answer 1

We have

`cos(sec^-1x+\text(cosec)^-1x)`

`=cos  pi/2`    `[becausesec^-1x+\text(cosec)^-1x=pi/2]`

= 0

 

`thereforecos(sec^-1x+\text(cosec)^-1x)=0`  , ∣ x ∣ ≥1