## Trigonometry (11th Edition) Clone

$$\pm\sqrt{\frac{1-\cos\frac{3\theta}{5}}{2}}=\sin\frac{3\theta}{10}$$
$$\pm\sqrt{\frac{1-\cos\frac{3\theta}{5}}{2}}$$ From the half-angle identity for sine: $$\pm\sqrt{\frac{1-\cos A}{2}}=\sin\frac{A}{2}$$ We can apply the identity to the given expression with $A=\frac{3\theta}{5}$. $$\pm\sqrt{\frac{1-\cos\frac{3\theta}{5}}{2}}=\sin\frac{\frac{3\theta}{5}}{2}$$ $$\pm\sqrt{\frac{1-\cos\frac{3\theta}{5}}{2}}=\sin\frac{3\theta}{10}$$