# What is the proof of the half-angle formula?

##### 1 Answer

Apr 25, 2015

Assuming that you have the Double Angle Formula for Cosine:

and the Pythagorean Formula for Sines and Cosines:

**The Half Angle Formula for Cosine**

follows directly from the Double Angle Formula for Cosine:

**The Half Angle Formula for Sine**

is developed from the Half Angle Formula for Cosine (and the Pythagorean Formula)

Other half Angle Formulae can be developed from these.

(Caution: If converting these "squared" half angle functions by taking the square roots, be sure to adjust the sign for the quadrant of the angle)