To solve this trigonometric equation, we'll first rewrite the equation using the Pythagorean identity sin^2(x) + cos^2(x) = 1.

Given: sin(πcosx) = cos(πsinx)

Rewrite as: sin(πcosx) = sin(π/2 - πsinx)

Now using the angle addition formula for sine: sin(A - B) = sin(A)cos(B) - cos(A)sin(B)

sin(πcosx) = sin(π/2)cos(πsinx) - cos(π/2)sin(πsinx)
sin(πcosx) = 1cos(πsinx) - 0sin(πsinx)
sin(πcosx) = cos(πsinx)

Therefore, the given trigonometric equation sin(πcosx) = cos(πsinx) is satisfied.