The half angle formula deal with fractions and square roots. The Blogger text software doesn't have good ways to type those in, so I resort to using pictures with captions.
These are the original half angle formulas.
This is a step by step (across) way to turn the sine and cosine of 15 degrees into fractions with whole number denominators. These answers look different from the ones you get using subtraction of angles, either 60 degrees - 45 degrees or 45 degrees - 30 degrees. If you type in the formulas, you get the same answers on your calculators.
This is a step by step (across) way to turn the sine and cosine of 22.5 degrees into fractions with whole number denominators.
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