# Solve frac{(1-sin^{2}x)}{(csc^{2}x-1)}

Question
Solve $$\frac{(1-\sin^{2}x)}{(csc^{2}x-1)}$$

2021-01-18
$$\frac{(1-\sin^{2}(x))}{csc^{2}(x)-1}$$
Use the following identity: $$\cos^{2}(x)+\sin^{2}(x)=1$$
Therefore $$1-\sin^{2}\frac{(x)=cos^{2}(x)}{(-1+csc^{2}(x))}$$
Use the following identity: $$-\cot^{2}(x)+csc2(x)=1$$
Therefore $$-1+csc^{2}(x)=\cot^{2}(x)=\frac{\cos^{2}(x)}{\cot^{2}(x)}$$
Therefore
$$\frac{(1-\sin^{2}(x)}{(csc^{2}(x)-1)}=\frac{\cot^2(x)}{\cot^2(x)}$$

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