In △ ABC, the edges corresponding to angles a, B and C are a, B, C, a = 23, Tana + B2 + tanc2 = 4, 2sinbcosc = Sina respectively. Find a, B and B, C

In △ ABC, the edges corresponding to angles a, B and C are a, B, C, a = 23, Tana + B2 + tanc2 = 4, 2sinbcosc = Sina respectively. Find a, B and B, C

From Tana + B2 + tanc2 = 4, we can get cotc2 + tanc2 = 4 ｛ cosc2sinc2 + sinc2cosc2 = 4 ｛ 1sinc2cosc2 = 4 ｛ sinc = 12, and C ∈ (0, π) ｛ C = π 6, or C = 5 π 6, from 2sinbcosc = Sina, we can get 2sinbcosc = sin (B + C), that is sin (B-C) = 0 ｛ B = C = π 6A = π − (B + C) = 2 π 3. From sine theorem Asina = bsinb B = csinc, we can get b = C asinbsina = 23 × 1232 = 2