How to prove that {$\sin(x) , \sin(2x) , \sin(3x) ,...,\sin(nx)$} is independent in $\mathbb{R}$?
138343
How to prove that the set $\{\sin(x),\sin(2x),...,\sin(mx)\}$ is linearly independent?
143072
Proving $|\sin x - \sin y| < |x - y|$
13162
Prove $\alpha \in R[[x]]$ is a unit iff $a_0 \in R$ is a unit
109228
Prove that $v, Tv, T^2v, ... , T^{m-1}v$ is linearly independent
83173
Prove linear combinations of logarithms of primes over $\mathbb{Q}$ is independent
66500
Proving that orthogonal vectors are linearly independent
94580
Prove that, $\binom{3n}{r}=\binom{3n-1}{r} + \binom{3n-1}{r-1}$
92600
Let $V$ be a $K$-vector space, $f: V \rightarrow V$ a linear map. Under some condition, show that $v, f(v),...,f^n(v)$ are linearly independent.
89186
Showing that $\frac{X_{(i)}}{X_{(n)}},i=1,2,...,n-1$ and $X_{(n)}$ are independent for a population with df $F(y)=y^{\theta}$
73047
Proving surjectivity of $\cos(z)$ and $\sin(z)$ and find all $z : \cos(z) \in \mathbb R$ and all $z: \sin(z) \in \mathbb R$
76884
Are $X$ and $X+Y$ independent, if $X$ and $Y$ are independent?
23617
Determine whether $f(x)={\sin x \over x}$ is uniformly continuous in $\mathbb R$
19973
If $X$ and $Y$ are independent $N(0,\sigma^2)$, then $X^2+Y^2$ and $X/Y$ are independent?
121558
Showing that $n$ exponential functions are linearly independent.
141273
When is $\sin(x)$ rational?
127052
Independence of non-constant real variables
126963
Is the sum of two variables independent of a third variable, if they are so on their own?