Prove that sin^4x - cos^4x = 2sin^2x - 1

Step-by-step explanation:

Step 1: From the given equation, taking the Left Hand Side (LHS) of the equation

Step 2: Simplify the LHS to make it equal to the Right Hand Side (RHS)

LHS = sin^4x - cos^4x = (sin²x) ² - (cos²x) ²

= (sin²x - cos²x) (sin²x + cos²x)

= sin²x - (1 - sin²x) since sin²x + cos²x = 1

= 2 sin²x - 1

= RHS

Hence proved.