Learn how to solve problems step by step online. Prove the trigonometric identity (sin(a)-cos(a))^2+(sin(a)+cos(a))^2=2. Starting from the left-hand side (LHS) of the identity. A binomial squared (difference) is equal to the square of the first term, minus the double product of the first by the second, plus the square of the second term. In other words: (a-b)^2=a^2-2ab+b^2. Applying the pythagorean identity: \sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1. Simplify -2\sin\left(a\right)\cos\left(a\right) using the trigonometric identity: \sin(2x)=2\sin(x)\cos(x).

Prove the trigonometric identity (sin(a)-cos(a))^2+(sin(a)+cos(a))^2=2