In the acute angle △ ABC, the opposite sides of the inner angles a, B and C are a, B and C respectively. It is known that C = 2, 2sin2c-2cos2c = 1. Find (1) the radius of the circumscribed circle of △ ABC; (2) when B = 5 π 12, find the size of A

In the acute angle △ ABC, the opposite sides of the inner angles a, B and C are a, B and C respectively. It is known that C = 2, 2sin2c-2cos2c = 1. Find (1) the radius of the circumscribed circle of △ ABC; (2) when B = 5 π 12, find the size of A

(1) From 2sin2c-2cos2c = 1, there are: cos2c = cos2c − sin2c = − 12 (3 points) (1 can also be changed into 1 = sin2c + cos2c, which can be converted into Tanc to solve C) ∵ C ∈ (0, π 2) ∵ 2C = 2 π 3, thus there are: C = π 3 (6 points) ∵ ABC circumscribed circle diameter 2R = csinc = 433, radius length 233. (8 points) ∵ ABC circumscribed circle diameter 2R = csinc = 433, radius length 233