Find the exponential generating function for the number of alphanumeric strings of length n n formed from the 26 26 uppercase le
tters of the English alphabet and 10 10 decimal digits if each vowel must appear at least one time; the letter T T must appear at least three times; the letter Z Z may appear at most three times; each even digit must appear an even number of times; and each odd digit must appear an odd number of times.
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first off, make sure you have a Unit Circle, if you don't do get one, you'll need it, you can find many online.
let's double up 67.5°, that way we can use the half-angle identity for the cosine of it, so hmmm twice 67.5 is simply 135°, keeping in mind that 135° is really 90° + 45°, and that whilst 135° is on the 2nd Quadrant and its cosine is negative 67.5° is on the 1st Quadrant where cosine is positive, so