sin(π/6)cos(5π/6) + sin(5π/6)cos(π/6) =
(sin(π/6)cos(5π/6)) + (sin(5π/6)cos(π/6))
Так как sin(π/6) = 1/2, cos(5π/6) = -√3/2, sin(5π/6) = -1/2, и cos(π/6) = √3/2, мы можем заменить значения:
(1/2)(-√3/2) + (-1/2)(√3/2) =
-√3/4 - √3/4 =
-2√3/4 =
-√3/2
Итак, упрощенный ответ равен -√3/2.
sin(π/6)cos(5π/6) + sin(5π/6)cos(π/6) =
(sin(π/6)cos(5π/6)) + (sin(5π/6)cos(π/6))
Так как sin(π/6) = 1/2, cos(5π/6) = -√3/2, sin(5π/6) = -1/2, и cos(π/6) = √3/2, мы можем заменить значения:
(1/2)(-√3/2) + (-1/2)(√3/2) =
-√3/4 - √3/4 =
-2√3/4 =
-√3/2
Итак, упрощенный ответ равен -√3/2.