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Question
\frac{1-\sin\left(x^{2}\right)}{\csc\left(x^{2}\right)-1}
Simplify the expression
\sin\left(x^{2}\right)
Evaluate
\frac{1-\sin\left(x^{2}\right)}{\csc\left(x^{2}\right)-1}
Transform the expression
More Steps
Evaluate
\csc\left(x^{2}\right)-1
\text{Use }\csc t = \frac{1}{\sin t}\text{ to transform the expression}
\frac{1}{\sin\left(x^{2}\right)}-1
Reduce fractions to a common denominator
\frac{1}{\sin\left(x^{2}\right)}-\frac{\sin\left(x^{2}\right)}{\sin\left(x^{2}\right)}
Write all numerators above the common denominator
\frac{1-\sin\left(x^{2}\right)}{\sin\left(x^{2}\right)}
\frac{1-\sin\left(x^{2}\right)}{\frac{1-\sin\left(x^{2}\right)}{\sin\left(x^{2}\right)}}
Multiply by the reciprocal
\left(1-\sin\left(x^{2}\right)\right)\times \frac{\sin\left(x^{2}\right)}{1-\sin\left(x^{2}\right)}
\text{Cancel out the common factor }1-\sin\left(x^{2}\right)
1\times \sin\left(x^{2}\right)
Solution
\sin\left(x^{2}\right)
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