Question

prove that :
$2 \: {sin}^{2} + {cos}^{4} = 1 + {sin}^{4}$
2 sinA^2 + cosA^4 = 1 + sinA^4

Answer 1

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Here is your answer...✌

To Prove :

2sin²A + cos⁴A = 1 + sin⁴A

Proof :

LHS

= 2sin²A + cos⁴A

= 2sin²A + ( cos²A )²

= 2sin²A + ( 1 - sin²A )²

= 2sin²A + 1 + ( sin²A )² - 2sin²A

= 1 + sin⁴A

= RHS [ Proved ]