It is known that a = A & # 178; - 2b + π / 2, B = B & # 178; - 2C + π / 2, C = C & # 178; - 2A + π / 2, where a, B and C are real numbers, Verification: at least one of a, B and C is positive

It is known that a = A & # 178; - 2b + π / 2, B = B & # 178; - 2C + π / 2, C = C & # 178; - 2A + π / 2, where a, B and C are real numbers, Verification: at least one of a, B and C is positive

Suppose all the three numbers are less than or equal to 0, then: a + B + C = [A & # 178; - 2b + π / 3] + [B & # 178; - 2C + π / 2] + [C & # 178; - 2A + π / 6] = [a & # 178; - 2A + 1] + [B & # 178; - 2b + 1] + [C & # 178; - 2C + 1] + π - 3 = (A-1) &# 178; + (B-1) &# 178; + (...)