Sin^2 (arctg 3-arctg (1/2))=1/2

Sin^2 (arctg3-arctg (1/2))= Sin(arctg3-arctg (1/2))*Sin(arctg3-arctg (1/2))= =( Sin(arctg3)Cos(arctg(1/2)) -Cos(arctg3)Sin(arctg(1/2)) )² Считаем по отдельности: а)Sin(arctg3) = 3/√(1 +9) = 3√10/10 б)Сos(arctg(1/2)) = 1/√(1 + 1/4) = 2√5/5 в)Сos(arctg3) =1/√10 = √10/10  г)Sin(arctg(1/2) = 1/2/√5/4 = √5/5 Теперь наш пример: (3√10/10 *  2√5/5 - √10/10  * √5/5)² = (6√50/50 - √50/50)²= (5√50/50)²= =(√50/10)² = 50/100 = 0,5