Final Answer
Step-by-step Solution
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Starting from the left-hand side (LHS) of the identity
Factor the polynomial $\sin\left(x\right)-\sin\left(x\right)^3$ by it's greatest common factor (GCF): $\sin\left(x\right)$
Learn how to solve trigonometric identities problems step by step online.
$\frac{\sin\left(x\right)-\sin\left(x\right)^3}{\cos\left(x\right)^2}$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (sin(x)-sin(x)^3)/(cos(x)^2)=1/csc(x). Starting from the left-hand side (LHS) of the identity. Factor the polynomial \sin\left(x\right)-\sin\left(x\right)^3 by it's greatest common factor (GCF): \sin\left(x\right). Applying the sine identity: \displaystyle\sin\left(\theta\right)=\frac{1}{\csc\left(\theta\right)}. Multiply the fraction and term.