To simplify the expression, we can use the trigonometric identity:

sin^2(x) + cos^2(x) = 1

By rearranging the terms, we get:

sin^2(x) = 1 - cos^2(x)

We can use this identity to simplify the expression:

24(sin^2(17) - cos^2(17)) / cos(34)

= 24[(1 - cos^2(17)) - cos^2(17)] / cos(34)

= 24(1 - 2cos^2(17)) / cos(34)

Now, we can use another trigonometric identity:

cos(2x) = 1 - 2sin^2(x)

By rearranging the terms, we get:

sin^2(x) = (1 - cos(2x)) / 2

We can use this identity to simplify further:

24(1 - 2cos^2(17)) / cos(34)

= 24(1 - cos(2*17)) / 2cos(34)

= 24sin^2(17) / cos(34)

= 24tan(17)

Therefore, the simplified expression is 24tan(17).