Answer
in the figure, sin ∠mqp =
a. cos n and sin r
b. sin r and sin n
c. cos n and sin m
d. cos r and sin n

The easiest way to get this problem correctly is by calculating the sines and cosines of all the angles in the choices then choosing the correct choice.

sin ∠MQP = sin(56) = 0.829
cos ∠N = cos(56) = 0.559
sin ∠R = sin(34) = 0.559
sin ∠N = sin(56) = 0.829
cos ∠N = cos(56) = 0.559
sin ∠M = sin(90) = 1
cos ∠R = cos(34) = 0.828

Based on these findings, it is obvious that sin ∠MQP is equal to cos ∠R and sin ∠N.
Thus, the correct choice is "d".