Sin 2 sin ²A / 2 cos^2 - cos A= tan A
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Answer:
2 cos 2A + sin²2A + 4 sin⁴A = 2
2(2 cos²A - 1) + (1 - cos²2A) + 4 sin⁴A = 2
4 cos²A - 2 + (1 - (2 cos²A - 1)²) + 4 sin⁴A = 2
4 cos²A - 2 + (1 - (4 cos⁴A - 4 cos²A + 1)) + 4 sin⁴A = 2
4 cos²A - 2 + 1 - 4 cos⁴A + 4 cos²A - 1 + 4 sin⁴A = 2
8 cos²A + 4(sin⁴A - cos⁴A) - 2 = 2
8 cos²A + 4(sin²A + cos²A)(sin²A - cos²A) - 2 = 2
8 cos²A + 4(sin²A - cos²A) - 2 = 2
8 cos²A + 4 sin²A - 4 cos²A - 2 = 2
4 sin²A + 4 cos²A - 2 = 2
4(sin²A + cos²A) - 2 = 2
4 - 2 = 2
2 = 2
Proved!
Step-by-step explanation:
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