Find the principal value of `cosec^(-1)(-2)`

Explanation

To find the principal value of \( \csc^{-1}(-2) \), we can follow these steps:

### Step 1: Understand the definition of \( \csc^{-1}(x) \)
The function \( \csc^{-1}(x) \) is defined for \( x \) such that \( |x| \geq 1 \). This means that \( \csc^{-1}(-2) \) is valid since \(-2\) falls within this range.

### Step 2: Relate \( \csc^{-1}(x) \) to \( \sin^{-1}(x) \)
We know that:
\[
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