Question

Sa se demonstreze inegalitatiile.Din imagine

Answer 1

[tex]\mbox{Ne folosim de faptul ca sinx si cosx}\in [-1, 1]\\ -1 \leq cosx \leq 1 | *(-1)\\ 1 \geq -cosx \geq -1\\ -1 \leq -cosx \leq 1 | + 5\\ 4 \leq 5-cosx \leq 6\\\\ 0 \leq |sinx| \leq 1\:\:| *2\\ 0 \leq 2|sinx| \leq 2\:\:|+1\\ 1 \leq 1+2|sinx| \leq 3\\\\ -1 \leq cosx \leq 1\:\:|*3\\ -3 \leq 3cosx \leq 3\:\:|+5\\ 2 \leq 3cosx +5 \leq 8 \\ \frac{1}{2} \geq \frac{1}{3cosx +5} \geq \frac{1}{8} [/tex]