The number of roots of the equation,

$(81)^{\sin ^{2} x}+(81)^{\cos ^{2} x}=30$

$(81)^{\sin ^{2} x}+\frac{(81)^{1}}{(18)^{\sin ^{2} x}}=30$

$(81)^{\sin ^{2} x}=t$

$t+\frac{81}{t}=30$

$\mathrm{t}^{2}-30 \mathrm{t}+81=0$

$(\mathrm{t}-3)(\mathrm{t}-27)=0$

$(81)^{\sin ^{2} x}=3^{1} \quad$ or $(81)^{\sin ^{2} x}=3^{3}$

$3^{4 \sin ^{2} x}=3^{1} \quad$ or $\quad 3^{4 \sin ^{2} x}=3^{3}$

$\sin ^{2} x=\frac{1}{4}$ or $\quad \sin ^{2} x=\frac{3}{4}$