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

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

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

Answers (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
\(\frac{(1-\sin^{2}(x)}{(csc^{2}(x)-1)}=\frac{\cot^2(x)}{\cot^2(x)}\)
0

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