prove that cos⁴A-cos²A=sin⁴A-sin²A
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Solution:
LHS = cos⁴ A - cos² A
= cos²A( cos² A - 1 )
= ( 1 - sin² A )[ -( 1 - cos² A ) ]
= ( 1 - sin² A ) ( - sin² A )
= - sin² A + sin⁴ A
= sin⁴ A - sin² A
= RHS
••••
LHS = cos⁴ A - cos² A
= cos²A( cos² A - 1 )
= ( 1 - sin² A )[ -( 1 - cos² A ) ]
= ( 1 - sin² A ) ( - sin² A )
= - sin² A + sin⁴ A
= sin⁴ A - sin² A
= RHS
••••
sahana21:
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