sin 7П/12-sin П/12

To simplify the expression sin(7π/12) - sin(π/12), we can use the trigonometric identity:

sin(A - B) = sin(A)cos(B) - cos(A)sin(B)

Let's use this identity to simplify the expression:

sin(7π/12) - sin(π/12) = sin(6π/12 + π/12) - sin(π/12)
= sin(π/2)cos(π/12) - cos(π/2)sin(π/12)
= 1 * (√3/2) - 0 * (1/2)
= √3/2

Therefore, sin(7π/12) - sin(π/12) simplifies to √3/2.