this is because csc(3600) is undefined.
sec(-3600) is equal to 1.
1 + undefined is undefined.
you can solve this graphically or by formula.
the graph of csc(3600) is shown below:
the graph of sec(-3600) is shown below:
you can see from the graph that csc(3600) is undefined.
if one part of the answer is undefined, then the whole answer is undefined as far as i know.
by formula, you would solve for csc(3600) as follows:
360 degrees is one full cycle.
if you start at 3600 degrees and keep subtracting 360 degrees until your angle is between 0 and 360 degrees, you will find that 3600 - 10 * 360) = 3600 - 3600 = 0 degrees.
csc(0) degrees is equal to 1/sin(0) degrees is equal to 1/0 which is undefined.
sec(-3600) is analyzed as follows:
you want to keep adding 360 degrees until it turns positive.
-3600 + 10*3600 = 0 degrees.
sec(-3600) is equivalent to sec(0).
sec(0) is equal to 1 / cos(0) which is equal to 1/1 which is equal to 1.
csc(3600) = undefined.
sec(-3600) = 1
csc(3600) + sec(-3600) = undefined + 1 = undefined.
the graph confirms that to the best of my knowledge.