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

Prove the trigonometric identity (1-tan(x)^2)/(1+tan(x)^2)=cos(2x)