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

Solve $\frac{\left(1-{\mathrm{sin}}^{2}x\right)}{\left(cs{c}^{2}x-1\right)}$
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averes8
$\frac{\left(1-{\mathrm{sin}}^{2}\left(x\right)\right)}{cs{c}^{2}\left(x\right)-1}$
Use the following identity: ${\mathrm{cos}}^{2}\left(x\right)+{\mathrm{sin}}^{2}\left(x\right)=1$
Therefore $1-{\mathrm{sin}}^{2}\frac{\left(x\right)=co{s}^{2}\left(x\right)}{\left(-1+cs{c}^{2}\left(x\right)\right)}$
Use the following identity: $-{\mathrm{cot}}^{2}\left(x\right)+csc2\left(x\right)=1$
Therefore $-1+cs{c}^{2}\left(x\right)={\mathrm{cot}}^{2}\left(x\right)=\frac{{\mathrm{cos}}^{2}\left(x\right)}{{\mathrm{cot}}^{2}\left(x\right)}$
Therefore
$\frac{\left(1-{\mathrm{sin}}^{2}\left(x\right)}{\left(cs{c}^{2}\left(x\right)-1\right)}=\frac{{\mathrm{cot}}^{2}\left(x\right)}{{\mathrm{cot}}^{2}\left(x\right)}$