To simplify the expression sin(30+a)cos a - cos(30+a)sin a, we first use the angle sum formula for sine:
sin(α + β) = sin α cos β + cos α sin β
Applying the formula to our expression, we have:
sin(30+a)cos a - cos(30+a)sin = sin 30 cos a + cos 30 sin a - cos 30 sin a - sin 30 cos = 0
Therefore, the simplified expression is 0.
To simplify the expression sin(30+a)cos a - cos(30+a)sin a, we first use the angle sum formula for sine:
sin(α + β) = sin α cos β + cos α sin β
Applying the formula to our expression, we have:
sin(30+a)cos a - cos(30+a)sin
= sin 30 cos a + cos 30 sin a - cos 30 sin a - sin 30 cos
= 0
Therefore, the simplified expression is 0.