Sin8A+Cot8A=1-4Sin2A.Cos2A+2Sin4A.Cos4A

1.	Sin8A+Cot8A=1-4Sin2A.Cos2A+2Sin4A.Cos4A
Answer» (sin² A + cos² A)² = 1² sin⁴ A + 2sin²A cos² A +cos⁴ A = 1 You need to isolate the sum sin⁴ A + cos⁴ A to the left side such that: sin⁴ A + cos⁴ A = 1 - 2sin²A cos² A You need to raise to square both sides such that: (sin⁴ A + cos⁴ A) = (1 - 2sin²A cos² A)² sin⁸ A + 2sin⁴ Acos⁴ A + cos⁸ A = 1 - 4sin²A cos² A + 4sin⁴ A cos⁴ A Moving to the right 2sin⁴ Acos⁴ A yields: sin⁸ A +cos⁸ A = 1 - 4sin²A cos² A + 4sin⁴ A cos⁴ A - 2sin⁴ Acos⁴ A sin⁸ A + cos⁸ A = 1 - 4sin²A cos² A + 2sin⁴ A cos⁴ A

Answer»

(sin² A + cos² A)² = 1²

sin⁴ A + 2sin²A cos² A +cos⁴ A = 1

You need to isolate the sum sin⁴ A + cos⁴ A to the left side such that:

sin⁴ A + cos⁴ A = 1 - 2sin²A cos² A

You need to raise to square both sides such that:

(sin⁴ A + cos⁴ A) = (1 - 2sin²A cos² A)²

sin⁸ A + 2sin⁴ Acos⁴ A + cos⁸ A = 1 - 4sin²A cos² A + 4sin⁴ A cos⁴ A

Moving to the right 2sin⁴ Acos⁴ A yields:

sin⁸ A +cos⁸ A = 1 - 4sin²A cos² A + 4sin⁴ A cos⁴ A - 2sin⁴ Acos⁴ A

sin⁸ A + cos⁸ A = 1 - 4sin²A cos² A + 2sin⁴ A cos⁴ A

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Sin8A+Cot8A=1-4Sin2A.Cos2A+2Sin4A.Cos4A

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