CBSE BOARD XII, asked by Pakhi44, 1 year ago

Prove cos⁴A - cos²A = sin⁴A - sin²A.

Answers

Answered by Anonymous
15

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

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Answered by priyasingh123
10
HERE WE GO!!

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

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