Question

Sin⁴A-cos⁴A+1=2sin²A

Answer 1

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

Answer 2

Hi...☺

Here is your answer...✌
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LHS

= Sin⁴A - Cos⁴A +1

= (Sin²A)²-(Cos²A)² +1

= (Sin²A+Cos²A).(Sin²A-Cos²A)+1

= 1.(Sin²A-Cos²A)+1

= Sin²A-Cos²A+1

= Sin²A+1-Cos²A

= Sin²A+Sin²A

= 2Sin²A

= RHS

Hence proved