Use the elementwise operators (preceed divide/multiply with a dot).
x = 1:100;
y = sin(x).*cos(2*x)./tan(x).^2;
Addition and subtraction don't need the periods, but you'll have to ensure that the vectors you're combining have the same size. If you're using a scalar in an operation, MATLAB will automatically broadcast it across the array (see the 2 in the cosine term).
Any functions you call and pass the vector will need to be able to operate on a vector (most built-ins will), or you can use arrayfun() to wrap the function and apply it to each value indivudally. (Or use a for loop). The syntax is:
z = arrayfun(@(x) my_scalar_fun(x), y)