Question

sin²a +cos⁴a = cos²a +sin⁴a
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Answer 1

Answer:

How to prove 2 sin^2 A + cos^4 A = 1 + sin^4 A?

LHS = 2 sin^2A + cos^4 A

= 2 sin^2 A + (cos^2 A)^2

= 2 sin^2 A + (1 - sin^2 A)^2

= 2 sin^2 A + 1 - 2sin^2 A + sin^4A

= 1 + sin^4 A

= RHS.

Proved.

Answer 2

Step-by-step explanation:

sin²a +cos⁴a = cos²a +sin⁴a

or, cos⁴a - cos²a = sin⁴a - sin²a

LHS RHS

LHS = cos⁴A - cos²A

= cos²A( cos²A-1)

= (1 - sin²A )[ -( 1 - cos²A)]

= (1 - sin²A) ( - sin²A)

= - sin²A + sin⁴A

= sin⁴A - sin²A

= RHS

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