Answer:
We know that:
Sin(a + b) = sin(a)*cos(b) + sin(b)*cos(a)
Then if we use this property in our expression:
sin(a-30)-sin(a+30)
We get:
sin(a)*cos(-30°) + sin(-30°)*cos(a) - sin(a)*cos(30°) - sin(30°)*cos(a)
Now remember that:
sin(-x) = -sin(x)
and
cos(-x) = cos(x)
Then we can rewrite our expression as:
sin(a)*cos(30°) - sin(30°)*cos(a) - sin(a)*cos(30°) - sin(30°)*cos(a)
= -2*sin(30°)*cos(a)
and sin(30°) = 0.5
Then:
-2*sin(30°)*cos(a) = -2*0.5*cos(a) = -cos(a)
So we get:
sin(a-30)-sin(a+30)= - cos(a)
