Question

PROOF THAT: sin⁴a+cos⁴a=1-@2sin²a*cos²a

Answer 1

Solution:

//* We know that ,

i) a²+b² = (a+b)²-2ab

ii) sin²A + cos²A = 1 *//

Now ,

LHS = sin⁴A+cos⁴A

= (sin²A)²+(cos²A)²

= (sin²A+cos²A)²-2sin²Acos²A

= 1-2sin²Acos²A

= RHS

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