Prove the trigonometric identity $\frac{\csc\left(x\right)-\sin\left(x\right)}{\csc\left(x\right)+\sin\left(x\right)}=\frac{\cos\left(x\right)^2}{1+\sin\left(x\right)^2}$

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$\frac{\csc\left(x\right)-\sin\left(x\right)}{\csc\left(x\right)+\sin\left(x\right)}$

Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity (csc(x)-sin(x))/(csc(x)+sin(x))=(cos(x)^2)/(1+sin(x)^2). Starting from the left-hand side (LHS) of the identity. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}. Combine all terms into a single fraction with \sin\left(x\right) as common denominator. Multiply the single term \sin\left(x\right) by each term of the polynomial \left(\csc\left(x\right)+\sin\left(x\right)\right).