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

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$\frac{\sec\left(x\right)-\cos\left(x\right)}{\sec\left(x\right)+\cos\left(x\right)}$

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