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Apply the trigonometric identity: $\csc\left(\theta \right)^n$$=\frac{1}{\sin\left(\theta \right)^n}$, where $n=2$
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$\frac{\frac{1}{\sin\left(x\right)^2}-1}{\csc\left(x\right)^2}$
Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression (csc(x)^2-1)/(csc(x)^2). Apply the trigonometric identity: \csc\left(\theta \right)^n=\frac{1}{\sin\left(\theta \right)^n}, where n=2. Combine all terms into a single fraction with \sin\left(x\right)^2 as common denominator. Divide fractions \frac{\frac{1-\sin\left(x\right)^2}{\sin\left(x\right)^2}}{\csc\left(x\right)^2} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}. Applying the trigonometric identity: \sin\left(\theta\right)\cdot\csc\left(\theta\right)=1.