For example, let's try to construct
-5 = a(5sin^2(x)) + b(cos^2(x)) + c(tan(x))
where a, b, and c are constants.
Note that sin^2(x) + cos^2(x) = 1 is a constant, so let c = 0 and a = -1 and b = -5:
-1*(5sin^2(x)) + -5*(cos^2(x)) + 0*tan(x) = -5*(sin^2(x) + cos^2(x)) = -5*1 = -5
So a linear combination of two elements of the set makes a third element of the set. Thus the set is linearly dependent.