## Trigonometry (11th Edition) Clone

$$1-2\sin^222\frac{1^\circ}{2}=\frac{\sqrt2}{2}$$
$$1-2\sin^222\frac{1^\circ}{2}$$ 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 $1-2\sin^222\frac{1^\circ}{2}$. $$1-2\sin^222\frac{1^\circ}{2}=\cos\Big(2\times22\frac{1^\circ}{2}\Big)$$ $$1-2\sin^222\frac{1^\circ}{2}=\cos45^\circ$$ $$1-2\sin^222\frac{1^\circ}{2}=\frac{\sqrt2}{2}$$