Sure, let's simplify the given trigonometric expression step-by-step:
The given expression is:
[tex]\[
(\csc x)^2 - 1
\][/tex]
To simplify this, we will use a known trigonometric identity related to cosecant and cotangent.
1. Recall the identity for cosecant squared:
[tex]\[
(\csc x)^2 = 1 + (\cot x)^2
\][/tex]
2. Substitute the identity into the given expression:
[tex]\[
(\csc x)^2 - 1 = (1 + (\cot x)^2) - 1
\][/tex]
3. Simplify by subtracting 1:
[tex]\[
(1 + (\cot x)^2) - 1 = (\cot x)^2
\][/tex]
So, the simplified form of the expression [tex]\((\csc x)^2 - 1\)[/tex] is:
[tex]\[
(\cot x)^2
\][/tex]
Thus, the final simplified expression is:
[tex]\[
\boxed{(\cot x)^2}
\][/tex]
