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

Learn how to solve special products problems step by step online. Prove the trigonometric identity (1+cos(x))/(sin(x)^2)=1/(1-cos(x)). Starting from the left-hand side (LHS) of the identity. Applying the trigonometric identity: \sin\left(\theta \right)^2 = 1-\cos\left(\theta \right)^2. Factor the difference of squares 1-\cos\left(x\right)^2 as the product of two conjugated binomials. Simplify the fraction \frac{1+\cos\left(x\right)}{\left(1+\cos\left(x\right)\right)\left(1-\cos\left(x\right)\right)} by 1+\cos\left(x\right).