PROVE THAT :
Cos⁴A - Cos²A = Sin⁴A - Sin²A
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Hey there!
L.H.S:
Cos⁴A - Cos²A
= cos²A ( cos²A - 1)
= - cos²A ( 1 - cos²A)
= - (1-sin²A) sin²A {∵ 1- cos²A = sin²A}
= - sin²A + sin⁴A
= sin⁴ A - sin²A
= R.H.S
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