If the area of △ ABC is s = a # 178; - (B-C) # 178;, then Tan (A / 2)= A1/2 B1/4 C1/8 D1 | Math enthusiast | Mathematical art

If the area of △ ABC is s = a # 178; - (B-C) # 178;, then Tan (A / 2)= A1/2 B1/4 C1/8 D1

There is cosine theorem: A ^ 2 = B ^ 2 + C ^ 2-2bccosa, get: A ^ 2-B ^ 2-C ^ 2 = - 2bccosa, so: S = a ^ 2-B ^ 2-C ^ 2 + 2BC = 2BC (1-cosa) and by sine theorem: S = (bcsina) / 2, we can get: 4 (1-cosa) = Sina, that is: (1-cosa) / Sina = 1 / 4, by universal formula: Sina = 2

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