Answer
$$\cos75^\circ=\sqrt{\frac{1+\cos150^\circ}{2}}$$
22 goes with C.
Work Step by Step
$$\cos75^\circ$$
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.
