The least value of $4 {\sec }^2\mathrm{x}+25 {\mathrm{cosec}}^2\mathrm{x}$

$$\begin{gathered} {\text{⨍ (x)=4sec}}^2{\text{x+25 cosec}}^2\text{x} \\ {\text{⨍ (x)=4+4Tan}}^2{\text{x+25+25 cot}}^2\text{x} \\ \mathrm{A}.\mathrm{M}\ge \mathrm{G}.\mathrm{M} \\ \frac{4{\mathrm{Tan}}^2\mathrm{x}+25{\cot }^2\mathrm{x} }{2} \\ \ge \sqrt{4{\mathrm{Tan}}^2\mathrm{x}.}25{\cot }^2\mathrm{x} \\ 4{\mathrm{Tan}}^2\mathrm{x}+25{\cot }^2{\mathrm{x}}^1 \\ \ge 2\times 2\times 5 \\ \ge 20 \\ \text{⨍ (x)≥29+20} \\ \ge 49 \end{gathered}$$