Understanding the Half Angle Formulas
The half-angle formulas are:



Examples: Rewrite each expression to contain only first-degree functions:
1)

We must use the formula
to reduce the power. Notice that 45° is 


We could stop here, but if you remember that
we can go further:

2)



We could stop here, but if you remember that



We must use the formula
to reduce the power. Notice that
is 


3)





We aren't told what
equals in this expression, so we will work with it as is. Let's replace 

And since they have the same denominator we can subtract the numerators:

Next we'll distribute and combine like terms:


And reduce:

Practice: Rewrite each expression to contain only first-degree trig functions


And since they have the same denominator we can subtract the numerators:

Next we'll distribute and combine like terms:


And reduce:

1)

2)

3)

4)

5)

Answers:1)





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