Question

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

Answer 1

let us suppose that the following statement is true and sin²A + cos⁴A = cos²A + sin⁴A

then ,

=> sin²A-cos²A = sin⁴A-cos⁴A

=> sin²A-cos²A = (sin²A)²-(cos²A)1

=> sin²A - cos²A = (sin²A-cos²A)(sin²A+cos²A)

as , sin²A+cos²A = 1

then,
sin²A-cos²A = sin²A-cos²A

hence , our supposition is right
therefore , sin²A + cos⁴A = cos²A+sin⁴A

hope this helps