Question

How do you evaluate `sec^-1(sec((7pi)/10))`?

Answer 1

`(7pi)/10`

Explanation:

`sec^(-1)x` is defined for x`in(R-]-1,1[)rarr([0,pi]-{pi/2})`.
`sec^(-1)secx= x` if and only if x`in([0,pi]-{pi/2})`.
in your question, since `(7pi)/10in([0,pi]-{pi/2})`
so, `sec^(-1)sec((7pi)/10)=(7pi)/10`