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

Learn how to solve factor by difference of squares problems step by step online. Prove the trigonometric identity (1+sin(x))(1-sin(x))=cos(x)^2. Starting from the left-hand side (LHS) of the identity. The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: (a+b)(a-b)=a^2-b^2.. Apply the trigonometric identity: 1-\sin\left(\theta \right)^2=\cos\left(\theta \right)^2. Since we have reached the expression of our goal, we have proven the identity.