[latex] 7^{tgx} + 7^{ctg( \frac{ \pi }{2}+x )} \leq \frac{50}{7} [/latex]

[latex]7^{tgx}+7^{ctg(90+x)} \leq \frac{50}{7}\\ 7^{tgx}+7^{-tgx} \leq \frac{50}{7}\\ 7^{2tgx}+1 \leq \frac{50}{7}\\ 7^{2tgx}*7+7 \leq 50*7^{tgx}\\ 7^{tgx}=y\\ 7y^2-50y+7 \leq 0\\ D=2500-4*49=48^2\\ y_{1}=\frac{50+48}{14}=7\\ y_{2}=\frac{50-48}{14}=\frac{1}{7}\\ \\ 7^{tgx}=7\\ tgx=1\\ x=\frac{\pi}{4}+\pi*n\\ \\ 7^{tgx}=7^{-1}\\ tgx=-1\\ x=-\frac{\pi}{4}+\pi*n [/latex]