This expression can be simplified using the sum-to-product formulas for sine and cosine:
sin(a)cos(b) - cos(a)sin(b) = sin(a+b)
In this case, a = 7π/12 and b = π/12. Therefore, the expression simplifies to:
sin(7π/12 + π/12)
= sin(8π/12)
= sin(2π/3)
= √3/2
Therefore, Sin7π/12 cos π/12 - sin π/12 cos 7π/12 is equal to √3/2.
This expression can be simplified using the sum-to-product formulas for sine and cosine:
sin(a)cos(b) - cos(a)sin(b) = sin(a+b)
In this case, a = 7π/12 and b = π/12. Therefore, the expression simplifies to:
sin(7π/12 + π/12)
= sin(8π/12)
= sin(2π/3)
= √3/2
Therefore, Sin7π/12 cos π/12 - sin π/12 cos 7π/12 is equal to √3/2.