$\sin ^{2}\left(\cos ^{-1} \frac{1}{2}\right)-\cos ^{2}\left(\sin ^{-1} \frac{\sqrt{3}}{2}\right)$ এর মান-

$\begin{array}{l}\because \sin ^{2}\left(\cos ^{-1} \frac{1}{2}\right)-\cos ^{2}\left(\sin ^{-1} \frac{\sqrt{3}}{2}\right) \\=1-\cos ^{2}\left(\cos ^{-1} \frac{1}{2}\right)-\left\{1-\sin ^{2}\left(\sin ^{-1} \frac{\sqrt{3}}{2}\right)\right\} \\=1-\left\{\cos \left(\cos ^{-1} \frac{1}{2}\right)\right\}^{2}-1+\left\{\sin \left(\sin ^{-1} \frac{\sqrt{3}}{2}\right)\right\}^{2} \\=-\left(\frac{1}{2}\right)^{2}+\left(\frac{\sqrt{3}}{2}\right)^{2} \\=-\frac{1}{4}+\frac{3}{4} \\=\frac{-1+3}{4} \\=\frac{2}{4} \\=\frac{1}{2}\end{array}$