(Randomized algorithms) Write a program to “discover” trigonometric identities. Your program should test all combinations of the trigonometric expressions shown below and use a randomized algorithm to
detect the equalities. For your equality testing, generate random numbers in the to range.
(h) sin( t)
(i) cos( t)
(j) tan( t)
(l) 2 sin(t=2) cos(t=2)
(n) 1 cos2(t)
(o) 1 cos(2t)
(Backtracking) The partition problem consists of determining if there is a way to partition a set of integers
if S1 [S2 = S and S1 \S2 = fg. Write aP
S into two subsets S1 and S2 such that S1 =
S2. Recall that S1 and S2 are a partition of S if and only
function that solves the partition problem using backtracking. If a partition exists, your program should display it; otherwise it should indicate that no partition exists. For example, if S = f2; 4; 5; 9; 12g, your program should output the partition S1 = f2; 5; 9g and S2 = f4; 12g and if S = f2; 4; 5; 9; 13g your program should indicate that no partition exists.
Given the little time available, a demo will not be required, thus it is very important that your report accurately describes your work.