SOLUTION: How do I develop the identity for {{{sin(expr(1/2)a)}}} by using the identity for {{{cos (2a)}}}?

Question 451184: How do I develop the identity for by using the identity for ?
Answer by Edwin McCravy(20081) (Show Source): You can put this solution on YOUR website!




Start with the identity:







 <-- sometimes this is given. If so you can start here







Now substitute 



Do one cancellation on the right:





The sign to use depends on the quadrant
in which the terminal side of  lies. 

If the terminal side of  lies in the 
first or second quadrants, the identity uses the 
positive sign.

If the terminal side of  lies in the 
third or fourth quadrants, the identity uses the 
negative sign.

Edwin

RELATED QUESTIONS
How do I verify the identity of (1 + sin(y))[1 + sin(-y)] = cos^2(y) (answered by lwsshak3)
Verify the following identity by using an angle sum identity: cos(2x) = 1 �... (answered by Alan3354,stanbon)
how do i verify the identity of sin(x+pi/2)=cos x (answered by Alan3354,Edwin McCravy,ikleyn)
How do i complete the identity?... (answered by Edwin McCravy)
prove each identity, SHOW WORK a. cos(2(3.14)-A)=cos A b. sin((3(3.14)/2)-A)=-cosA (answered by jim_thompson5910)
Simplify the expression by using a double-angle formula. cos^2 (3pi/11) - sin^2... (answered by lwsshak3)
How do i establish the identity sin^3 theta - cos^3 theta/sin theta - cos theta = 1 +... (answered by dkppathak)
I have to verify the identity of... (answered by DrBeeee)
Verify the identity: (cos x-sin... (answered by robertb)