If ${81}^{{\sin }^2\mathrm{x}}+{81}^{{\cos }^2\mathrm{x}}=30, 0\le \mathrm{x}\le \frac{\mathrm{\pi }}{2}$ then $\mathrm{x}=$

$$\begin{gathered} {81}^{{\sin }^2\mathrm{x}}+{81}^{{\cos }^2\mathrm{x}}=30 \\ {81}^{{\sin }^2\mathrm{x}}+{81}^{1-{\sin }^2\mathrm{x}}=30 \\ {81}^{{\sin }^2\mathrm{x}}=\mathrm{t} \\ \mathrm{t}+\frac{81}{\mathrm{t}}=30 \\ {\mathrm{t}}^2-30\mathrm{t}+81=0 \\ (\mathrm{t}-27) (\mathrm{t}-3)=0 \\ \mathrm{t}=27, \mathrm{t}=3 \end{gathered}$$

$$\begin{gathered} {81}^{{\sin }^2\mathrm{x}}=3^3 \\ 4{\sin }^2\mathrm{x}=3 \\ {\sin }^2\mathrm{x}=\frac{3}{4} \\ {\sin }^2\mathrm{x}={\sin }^2\frac{\mathrm{\pi }}{3} \\ \mathrm{x}=\frac{\mathrm{\pi }}{3} \\ {81}^{{\sin }^2\mathrm{x}}=3^1 \\ {\sin }^2\mathrm{x}=1 \Rightarrow \mathrm{x}=\frac{\mathrm{\pi }}{2} \\ \mathrm{x}=\frac{\mathrm{\pi }}{3}, \frac{\mathrm{\pi }}{2} \end{gathered}$$