Proof Of The Double Angle And Half Angle Formulas

You must already know the addition formula for cos(j + k) and sin(j + k):

Let [k = j], now the above equation will be like this:

This is the addition the double angle formula. Since [cos²(j) + sin²(j) = 1], we obtain an alternative form of the double angle for [cos(2j)]:

Now lets use the above two equation to obtain the half angle formulas:

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