Question

solve it ⚠️


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Answer 1

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LHS = cos⁴ - cos²A

= cos²A( cos²A - 1 )

= ( 1 - sin²A )[ -( cos²A ) ]

= ( 1 - sin²A )( - sin²A )

= - sin²A + sin⁴A

= sin⁴ - sin²A

= RHS

Answer 2

L.H.S

$\implies$ Cos⁴A-Cos²A

$\implies$ Cos²A(Cos²A-1)

$\implies$ (1-sin²A){(1-Sin²A)-1}

$\implies$ (1-sin²A)(1-Sin²A-1)

$\implies$ (1-Sin²A)(-Sin²A)

$\implies$ -Sin²A+Sin⁴A

$\implies$ Sin⁴A-Sin²A = R.H.S

hence proved !