durga95 durga95

07-05-2019
Mathematics

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How do you prove 4 (cos^4A + sin^4A) / (3+cos4A) = (cos^4A-sin^4A) sec2A?

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kaylasandvick kaylasandvick

07-05-2019

Step-by-step explanation:

Step 1: (sin²A+cos²A)²

Step 2: (a+b)² = a²+b²+2ab

Step 3: (sin²A+cos²A)²=sin⁴+cos⁴+2sin²Acos²A

make sure to use: sin²a+cos²a=1

Step 4: (1)²-2sin²Acos²A = sin⁴A+cos⁴A

Step 5: 1-2sin²Acos²A = sin⁴A+cos⁴A

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