Evaluate each of the following: `"c o s e c"^(-1)("c o s e c"pi/4)`
(ii) `"c o s e c"^(-1)("c o s e c"(3pi)/4)`

Explanation

(i) `c o s e c^{-1}c o s e c` ` x=x`


Provided `x \in[\frac{-\pi}{2}, \frac{\pi}{2}]-\{0\}`

`\therefore` we can write `c o s e c^{-1}`
`c o s e c(\frac{\pi}{4})=\frac{\pi}{4}.`




(ii) `c o s e c^{-1}(c o s e c` `x)=x`

Provided `x \in[\frac{-\pi}{2}, \frac{\pi}{2}]-\{0\}`

`\therefore` we can write `c o s e c^{-1} c o s e c(\frac{3 \pi}{4})=\frac{3 \pi}{4}.`