In △ ABC, the edges of angles a, B and C are a, B and C respectively, and (a + B + C) (B + C-A) = 3bC. (1) find the degree of angle a; (2) if 2B = 3C, find the value of Tanc

In △ ABC, the edges of angles a, B and C are a, B and C respectively, and (a + B + C) (B + C-A) = 3bC. (1) find the degree of angle a; (2) if 2B = 3C, find the value of Tanc

(1) ∵ (a + B + C) (B + C-A) = 3bC, ∵ (B + C) 2-A2 = 3bC, ∵ A2 = B2 + C2 BC, obtained by cosine theorem: 2cosa = 1, ∵ cosa = 12, and 0 < a < π, ∵ a = π 3. (2) ∵ 2B = 3C, ∵ obtained by sine theorem: 2sinb = 3sinc, and a = π 3, ∵ B + C = π - a = 2 π 3, ∵ B = 2 π 3-C, ∵ 2Sin (2 π 3-C) = 3sinc, namely 2 [32cosc - (- 12) sinc] = 3sinc, ∵ Tanc = 32