Learn how to solve problems step by step online. Prove the trigonometric identity 2sin(a)^2-1=sin(a)^4-cos(a)^4. Starting from the right-hand side (RHS) of the identity. Factor the difference of squares \sin\left(a\right)^4-\cos\left(a\right)^4 as the product of two conjugated binomials. Applying the pythagorean identity: \sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1. Applying the pythagorean identity: \cos^2(\theta)=1-\sin(\theta)^2.

Prove the trigonometric identity 2sin(a)^2-1=sin(a)^4-cos(a)^4