Question

How do you prove `csc^-1(x)=pi/2 -sec^-1(x)`?

Answer 1

as below

Explanation:

Let `csc^-1x=theta`
`=>x=csctheta`
`=>x=sec(pi/2-theta)`
`=>sec^-1x=sec^-1sec(pi/2-theta)`
`=>sec^-1x=(pi/2-theta)`
`=>sec^-1x=(pi/2-csc^-1x)` [putting `theta=csc^-1x`]
`=>csc^-1x=(pi/2-sec^-1x)`
proved