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) to reduce the power. Notice that 45° is We could stop here, but if you remember that
we can go further:
We must use the formula 
to reduce the power. Notice that 
is 
3)to reduce the power. Notice that is 
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 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:
1)
2)
3)
4)
5)
Answers:1)
2) 
3) 
4) 
5) 
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