Prove $\forall p\in(0,1), \theta\in [0,\pi /2];\cos^p(\theta)≤\cos(p\theta)$
60761
Proof: $\cos^p (\theta) \le \cos(p\theta)$
129890
Proving inequality $|\sin(n\theta) |\le n\sin\theta$
131754
Prove $ \forall c \in \mathbb{R^{+}}, \forall B \in \mathbb{N}, \exists n \in \mathbb{N}, (n \geq B) \wedge (\sqrt{2n} > c \ln(n+2)) $?
103536
How to prove $|e^{i\theta} - 1| \leq |\theta|$?
46760
To show that $P(|X-Y| \leq 2) \leq 3P(|X-Y| \leq 1)$
62755
The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$
62239
For a polynomial $p(z)$, prove there exist $R>0$, such that if $|z|=R$, then $|p(z)|\geq |a_n|R^n/2$
125209
Prove $e^x - e^y \leq e |x-y|$ for $x$ belonging to $[0,1]$
25458
Prove inequalities $2\sqrt{n+1}-2 \leq 1 + 1/\sqrt{2} + 1/\sqrt{3} + .... + 1/\sqrt{n}\leq 2\sqrt{n}-1$
106767
$|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
96388
Prove $\sin(x)\tan(x) > x^2$ for $x \in ( \,0, \frac{\pi}{2}) \,$
95293
Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
117262
Proving a logarithm inequality
79969
Proof that a formula $\theta$ is valid if and only if $\forall x \theta$ is valid
3273
Trouble in proving that $\|x\|_p = \max|x_j|$
122115
Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
88687
Proof of the inequality $||a+b|^p - |a|^p| \leq \epsilon |a|^p + C_{\epsilon} |b|^p$