# sin(a/2)=- square root of (1-cos(a))/2

Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.
To remove the radical on the left side of the equation, square both sides of the equation.
Simplify the left side of the equation.
Solve for .
Move to the left side of the equation by subtracting it from both sides.
Simplify the left side.
Simplify each term.
Raise to the power of .
Multiply by .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
Multiply by .
Move .
Apply the cosine doubleangle identity.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Subtract from .
Divide by .
Since , the equation will always be true for any value of .
All real numbers
All real numbers
The result can be shown in multiple forms.
All real numbers
Interval Notation:
sin(a/2)=- square root of (1-cos(a))/2