To solve the equation sin(p/2-x) = sin(-p/4), we can use the trigonometric identity sin(-x) = -sin(x).

So sin(p/2-x) = -sin(p/4)

We know that sin(p/2 - x) = sin(p/2)cos(x) - cos(p/2)sin(x) by using the sum and difference formula.

sin(p/2 - x) = 1cos(x) - 0sin(x) = cos(x)

Now, we have cos(x) = -sin(p/4)

We know that sin(p/4) = sqrt(2)/2

Therefore, cos(x) = -sqrt(2)/2

Now, to solve 2cos(p/2-x) = √2:

We substitute cos(p/2-x) = -sqrt(2)/2 into the equation:

2*(-sqrt(2)/2) = √2

This simplifies to:

-√2 = √2

Since this is not true, the given equation has no solution.