Question 188012
*[Tex \LARGE \csc^2 (\theta) - \cot^2 (\theta)] ... Start with the given expression.



*[Tex \LARGE \frac{1}{\sin^2 (\theta)} - \frac{\cos^2(\theta)}{\sin^2 (\theta)}] ... Rewrite each term in terms of sines and cosines.



*[Tex \LARGE \frac{1 - \cos^2(\theta)}{\sin^2 (\theta)}] ... Combine the fractions.



*[Tex \LARGE \frac{\sin^2 (\theta)}{\sin^2 (\theta)}] ... Use the identity *[Tex \LARGE 1 - \cos^2(\theta)=\sin^2 (\theta)]



*[Tex \LARGE 1] Reduce



So *[Tex \LARGE \csc^2 (\theta) - \cot^2 (\theta)=1]