Question

Find the exact value by using a half-angle identity.

Answer 1

We can write this as,\[\large \cos\left(\frac{5\pi}{6\cdot2}\right) \qquad \rightarrow \qquad \cos\left(\frac{5\pi/6}{2}\right)\]And from here, we can apply our half-angle identity for cosine.

Answer 2

\[\large \cos\left(\frac{\theta}{2}\right)=\sqrt{\frac{1+\cos\theta}{2}}\]

Answer 3

\[\large \cos\left(\frac{5\pi/6}{2}\right)=\sqrt{\frac{1+\cos(5\pi/6)}{2}}\]Then just simplify!