Write each expression in factored form as an algebraic expression of a single trigonometric function.
-$\csc ^ { 2 } x - 1$
A) $( \csc x + 1 ) ( \csc x - 1 )$
B) $\cot x$
C) $( \cot x + 1 ) ( \cot x - 1 )$
D) $\csc x - 1$

Question

Quizplus · Accepted Answer

The expression $\csc^2 x - 1$ can be rewritten using the Pythagorean identity $\csc^2 x = 1 + \cot^2 x$, which simplifies to $\cot^2 x$. This can be factored as a difference of squares, $(\cot x + 1)(\cot x - 1)$, but since the question asks for an expression in terms of $\csc x$, the correct factored form is $(\csc x + 1)(\csc x - 1)$, using the identity in reverse.

Write Each Expression in Factored Form as an Algebraic Expression csc⁡2x−1\csc ^ { 2 } x - 1csc2x−1

Write Each Expression in Factored Form as an Algebraic Expression $\csc ^ { 2 } x - 1$