## Trigonometry (11th Edition) Clone

$$\cos75^\circ=\sqrt{\frac{1+\cos150^\circ}{2}}$$ 22 goes with C.
$$\cos75^\circ$$ We know that $75^\circ=\frac{150^\circ}{2}$ In other words, $75^\circ$ is the half angle of $150^\circ$. Thus, we might apply the half-angle identity here. - The half-angle identity for cosine: $$\cos\frac{\theta}{2}=\pm\sqrt{\frac{1+\cos\theta}{2}}$$ Therefore, $$\cos75^\circ=\pm\sqrt{\frac{1+\cos150^\circ}{2}}$$ $75^\circ$ lies in quadrant I, where cosines are positive. So $\cos75^\circ\gt0$, meaning that $$\cos75^\circ=\sqrt{\frac{1+\cos150^\circ}{2}}$$ That means 22 goes with C.