## Trigonometry (11th Edition) Clone

$$\sqrt{\frac{1-\cos40^\circ}{2}}=\sin20^\circ$$
$$X=\sqrt{\frac{1-\cos40^\circ}{2}}$$ Recall the half-angle identity for sine, which states $$\sqrt{\frac{1-\cos A}{2}}=\sin\frac{A}{2}$$ So we can apply the identity to $X$ with $A=40^\circ$, meaning that $$X=\sqrt{\frac{1-\cos40^\circ}{2}}=\sin\frac{40^\circ}{2}$$ $$X=\sin20^\circ$$ Therefore, $$\sqrt{\frac{1-\cos40^\circ}{2}}=\sin20^\circ$$ $\sin20^\circ$ is a single trigonometric function, so we can stop here.