Вычислите: sin105cos15 + sin15sin165 + tg225
Sin105*cos15 + sin15*sin165 + tg225 = sin(90+15)*cos15 + sin15*sin(90+75) + tg(180+45) = cos15*cos15 + sin15*cos75 - tg45 = cos^2 15 + sin15*cos(90-15) - 1 = cos^2 15 + sin15*sin15 - 1 = cos^2 15 + sin^2 15 - 1 = 1 - 1 = 0
tg(180° + 45°) = tg45°
Sin105⁰Cos15⁰ + Sin15⁰Sin165⁰ + tg225⁰ = Sin(90⁰ + 15⁰)Cos15⁰ +
+ Sin15⁰Sin(180⁰ - 15⁰) + tg(180⁰ + 45⁰) = Cos15⁰Cos15⁰ + Sin15⁰Sin15⁰ + tg45⁰ =
= (Cos²15⁰ + Sin²15⁰) + tg45⁰ = 1 + 1 = 2