Cos(n-t) +cos(n/2-t) /sin(2n-t) -sin(3n/2-t)

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To simplify this expression, we can use trigonometric identities to rewrite each term in a more convenient form.

Starting with the first term, cos(n-t):

cos(n-t) = cos(n)cos(t) + sin(n)sin(t)

Next, the second term, cos(n/2-t):

cos(n/2-t) = cos(n/2)cos(t) + sin(n/2)sin(t)

For the denominator, sin(2n-t):

sin(2n-t) = sin(2n)cos(t) - cos(2n)sin(t)

And finally, sin(3n/2-t):

sin(3n/2-t) = sin(3n/2)cos(t) - cos(3n/2)sin(t)

Now, we can substitute these expressions into the main expression to get:

[cos(n)cos(t) + sin(n)sin(t) + cos(n/2)cos(t) + sin(n/2)sin(t)] / [sin(2n)cos(t) - cos(2n)sin(t) - sin(3n/2)cos(t) + cos(3n/2)sin(t)]

= [cos(n)cos(t) + cos(n/2)cos(t) + sin(n)sin(t) + sin(n/2)sin(t)] / [sin(2n)cos(t) - sin(3n/2)cos(t) - cos(2n)sin(t) + cos(3n/2)sin(t)]

This is the simplified form of the expression provided.