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Anton [14]
3 years ago
11

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

Mathematics
1 answer:
Liula [17]3 years ago
5 0

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.

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