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How do I know that the following equation is true:

How do I know that the following equation is true:-example-1
User Tobire
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Answer:

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.

User Burmat
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