Evaluate sin(p/4) cos(p/6) sin(p/6) cos(p/4)

To evaluate the expression sin(p/4) cos(p/6) sin(p/6) cos(p/4), we can start by using known values for the sine and cosine functions at these angles.

Firstly, we know:

• sin(p/4) = sqrt(2)/2
• cos(p/4) = sqrt(2)/2
• sin(p/6) = 1/2
• cos(p/6) = sqrt(3)/2

Now, substituting these values into the expression:

sin(p/4) cos(p/6) sin(p/6) cos(p/4) = (sqrt(2)/2) * (sqrt(3)/2) * (1/2) * (sqrt(2)/2)

This simplifies to:

= (sqrt(2) * sqrt(3) * 1 * sqrt(2)) / 16

And further simplifying gives:

= (2 * sqrt(3)) / 16 = sqrt(3) / 8

Thus, the final result is:

sin(p/4) cos(p/6) sin(p/6) cos(p/4) = sqrt(3) / 8