Answer
1=1
Work Step by Step
Step 1: Replace $\csc\theta$ with $\frac{1}{\sin\theta}$ and $\cot\theta$ with $\frac{\cos\theta}{\sin\theta}$
Hence,
$\csc^{2}\theta-\cot^{2}\theta=\frac{1}{\sin^{2}\theta}-\frac{\cos^{2}\theta}{\sin^{2}\theta}$
Step 2: Combine numerators with same denominator, hence,
$\csc^{2}\theta-\cot^{2}\theta = \frac{1-\cos^{2}\theta}{\sin^{2}\theta}$
Step 3: Since $\sin^{2}\theta+\cos^{2}\theta=1$, replace $(1-cos^{2}\theta)$ with $sin^{2}\theta$
Hence,
$\csc^{2}\theta-\cot^{2}\theta = \frac{\sin^{2}\theta}{\sin^{2}\theta}=1$
