Question

How do I know that the following equation is true:

Answer 1

Half angle Identity for cosine:

`$\cos \left((\theta)/(2) \right)=\pm \sqrt{(1+\cos(\theta))/(2) } $`

`\text{Note that it is} \pm \text{because we don't know which Quadrant the half-angle is, }`
`\text{the information of}\cos(\theta) \text{is not enough to conclude the angle}`

`$(\pi)/(8) \text{ is a Quadrant I angle, therefore, positive}$`

`$\cos \left((\pi)/(8) \right)=\sqrt{(1+\cos((\pi)/(4) ))/(2) } $`

The equation is true.