Question

Prove cos⁴A - cos²A = sin⁴A - sin²A.

Answer 1

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Answer 2

DETAILS :

Use a² - b² = ( a + b )( a - b )

Use sin²A + cos²A as 1

Then transpose to prove it .

sin⁴A - cos⁴A

= ( sin²A )² - ( cos²A )²

= ( sin²A + cos²A )( sin²A - cos² A )

= 1 ( sin²A - cos² A )

Hence : sin⁴A - cos⁴A = sin²A - cos²A

= cos⁴A - cos²A = sin⁴A - sin²A

Hence proved !