Trigonometry
Determine the exact value of the following trigonometric expression.
sin(3π4)cos(π12)−cos(3π4)sin(π12)\sin\left(\frac{3\pi}{4}\right)\cos\left(\frac{\pi}{12}\right)-\cos\left(\frac{3\pi}{4}\right)\sin\left(\frac{\pi}{12}\right)sin(43π)cos(12π)−cos(43π)sin(12π)
32\frac{\sqrt3}{2}23
−32-\frac{\sqrt3}{2}−23
12\frac1221
1