Final Answer
Step-by-step Solution
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Starting from the left-hand side (LHS) of the identity
Factor the polynomial $\csc\left(x\right)-\csc\left(x\right)\cos\left(x\right)^2$ by it's greatest common factor (GCF): $\csc\left(x\right)$
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$\csc\left(x\right)-\csc\left(x\right)\cos\left(x\right)^2$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity csc(x)-csc(x)cos(x)^2=sin(x). Starting from the left-hand side (LHS) of the identity. Factor the polynomial \csc\left(x\right)-\csc\left(x\right)\cos\left(x\right)^2 by it's greatest common factor (GCF): \csc\left(x\right). Apply the trigonometric identity: 1-\cos\left(\theta \right)^2=\sin\left(\theta \right)^2. Applying the cosecant identity: \displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}.