Răspuns:
c)
cos(x) - [cos(x)cos(60)-sin(x)sin(60)]+[cos(x)cos(120)-sin(x)sin(120)] =
= cos(x) - [cos(x)/2 - sin(x)√3/2]+[-cos(x)/2 - sin(x)√3/2] =
= cos(x) - cos(x)/2 + sin(x)√3/2 - cos(x)/2-sin(x)√3/2 =
= cos(x) - 2·cos(x)/2 =
= cos(x) - cos(x) =
= 0
d)
sin²(x+y) = [sin(x)cos(y)+cos(x)sin(y)]² =
= sin²(x)cos²(y) + cos²(x)sin²(y) + 2sin(x)cos(y)cos(x)sin(y) =
= sin²(x)[1-sin²(y)] + [1-sin²(x)]sin²(y) + 2sin(x)cos(y)cos(x)sin(y) =
= sin²(x)-sin²(x)sin²(y) + sin²(y)-sin²(x)sin²(y) + 2sin(x)cos(y)cos(x)sin(y) =
= sin²(x) + sin²(y) - 2sin²(x)sin²(y) + 2sin(x)cos(y)cos(x)sin(y) =
= sin²(x) + sin²(y) +2sin(x)cos(y)cos(x)sin(y) - 2sin(x)²sin(y)² =
= sin(x) + sin²(y) +2sin(x)sin(y)·[cos(y)cos(x) - sin(x)sin(y)] =
= sin²(x) + sin²(y) +2sin(x)sin(y)cos(x+y)
