cos(90°+x)cosx + sin(90°+x)sinx= cos(90°)cosx - sin(90°)sinx + sin(90°)sinx + cos(90°)cosx= 0cosx - 1sinx + 1sinx + 0cosx= -sinx + sinx= 0
Therefore, the value of the expression is 0.
cos(90°+x)cosx + sin(90°+x)sinx
= cos(90°)cosx - sin(90°)sinx + sin(90°)sinx + cos(90°)cosx
= 0cosx - 1sinx + 1sinx + 0cosx
= -sinx + sinx
= 0
Therefore, the value of the expression is 0.