Answer
$$1-2\sin^222\frac{1^\circ}{2}=\frac{\sqrt2}{2}$$
Work Step by Step
$$1-2\sin^222\frac{1^\circ}{2}$$
Just like the above exercises, recall that
$$1-2\sin^2A=\cos2A$$
Therefore, replace $A=22\frac{1^\circ}{2}$, we can apply the above identity to $1-2\sin^222\frac{1^\circ}{2}$.
$$1-2\sin^222\frac{1^\circ}{2}=\cos\Big(2\times22\frac{1^\circ}{2}\Big)$$
$$1-2\sin^222\frac{1^\circ}{2}=\cos45^\circ$$
$$1-2\sin^222\frac{1^\circ}{2}=\frac{\sqrt2}{2}$$
