Question

Prove that
sin⁴ A -cos⁴ A =2sin² A-1​

Answer 1

Sin⁴A+cos⁴A

(sin²A)² + (cos²A)²

(sin²A+cos²A)² - 2sin²Acos²A (: (a+b)² = a² + b² + 2ab)

(1)² - 2sin²Acos²A

1 - 2sin²Acos²A

Hence Proved

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