prove that: 2Sin²A + Cos²2A + 2Sin²A.Cos2A =1
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Step-by-step explanation:
2Sin²A + Cos²2A + 2Sin²A*Cos2A
2Sin²A(1 + Cos2A) + Cos²2A
2Sin²A*2Cos²A + (2Cos²A - 1)²
4Sin²A*Cos²A + 4Cos⁴A + 1 - 4Cos²A
4Cos²A(Sin²A + Cos²A) + 1 - 4Cos²A
4Cos²A + 1 - 4Cos²A
= 1
Hence proof
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