New posts in Cauchy Schwarz Inequality

Algebraic inequality $\sum \frac{x^3}{(x+y)(x+z)(x+t)}\geq \frac{1}{2}$

How do I prove this trigonometry inequality $\sin^2(y) \leq 2 \sin^2(x) + 2\sin^2(y-x)$?

Range of $\frac{\cos\theta_1+\cdots+\cos\theta_{10}}{\sin\theta_1+\cdots+\sin\theta_{10}}$ given $\sin^2\theta_1+\cdots+\sin^2\theta_{10}=1$

Prove a well-known inequality using Cauchy-Schwarz or AM-GM

Given positive numbers $x_1,...,x_n$ such that $x_1\cdots x_n=1$ prove that $\frac{1}{n-1+x_1}+\cdots+\frac{1}{n-1+x_n}\le 1$

Inequality with mean inequality

prove that $\sum_{cyc}\frac{a}{b^2+c^2}\ge \frac{4}{5}\sum_{cyc}\frac{1}{b+c}$

How do I show $(e^{x^2}-1)(e^{y^2}-1) \geq (e^{xy}-1)^2$ for all $x,y> 0$?

Inequality with a High Degree Constraint

When does equality hold in $\Bigr\lvert\sum_{k=1}^n a_kb_k\Bigr\rvert^2 \le \left(\sum_{k=1}^n |a_k|^2\right)\left(\sum_{k=1}^n |b_k|^2\right)$?